Conservation in the EU and all over the world aims at reducing biodiversity loss which has become a great issue in the last decades. However, despite existing efforts, Earth is assumed to face a sixth mass extinction. One major challenge for conservation is to reconcile the targets with conflicting interests, e.g. for food production in intensively used agricultural landscapes. Agriculture is an example of a coupled human-environment system that is approached in this thesis with the help of mathematical models from two directions. Firstly, the ecological subsystem is considered to find processes relevant for the effect of habitat connectivity on population abundances. Modelling theory predicts that the species-specific growth parameters (intrinsic growth rate and carrying capacity) indicate whether dispersal has a positive or negative effect on the total population size at equilibrium (r-K relationship). We use laboratory experiments in combination with a system of ordinary differential equations and deliver the first empirical evidence for a negative effect of dispersal on the population size in line with this theory. The result is of particular relevance for the design of dispersal corridors or stepping stones which are meant to increase connectivity between habitats. These measures might not be effective for biological conservation. A second population model, consisting of two coupled Ricker maps with a mate-finding Allee effect, is analyzed in order to examine the effect of bistability due to the Allee effect in combination with overcompensation in a spatial system. The interplay can cause complex population dynamics including multiple coexisting attractors, long transients and sudden population collapses. Essential extinction teaches us that not only small populations are prone to extinction but chaotic dynamics can drive a population extinct in a short period of time as well. By a comprehensive model analysis, we find that dispersal can prevent essential extinction of a population. In the context of conservation that is: habitat connectivity can promote rescue effects to save a population that exhibits an Allee effect. The two findings of the first part of this thesis have contrasting implications for conservation which shows that universal recommendations regarding habitat connectivity are impossible without knowledge of the specific system. Secondly, a model for the socio-economic subsystem is presented. Agri-environment schemes (AES) are payments that compensate farmers for forgone profits on the condition that they improve the ecological state of the agricultural system. However, classical economic models that describe the cost-effectiveness of AES often do not take the social network of farmers into account. Numerical simulations of the socio-economic model presented in this thesis suggest that social norms can hinder farmers from scheme participation. Moreover, social norms lead to multistability in farmers’ land-use decision behaviour. Informational campaigns potentially decrease the threshold towards more long-term scheme participation and might be a good tool to complement compensation payments if social norms affect land-use decisions. Finally, a coupled human-environment system is analyzed. An integrated economicecological model is studied to investigate the cost-effectiveness of AES if the species of concern exhibits an Allee effect. A numerical model analysis indicates large trade-offs between agricultural production and persistence probability. Moreover, conservation success strongly depends on the initial population size, meaning that conservation is well advised to start before the species is threatened. Spatial aggregation of habitat can promote rescue effects, suggesting land-sparing solutions for conservation. In that case,agglomeration bonuses may serve to increase the effectiveness of AES. Possible causes for population declines are diverse and can be a combination of human influences, e.g. due to habitat degradation and inherent ecosystem properties. That complicates the task of conservation. The models presented in this thesis simplify complex systems in order to extract processes relevant for biological conservation. The analysis of spatial effects and dynamical model complexity, e.g. due to Allee effects or a nonlinear utility function, allows us improve the understanding of coupled human-environment systems.

Neste trabalho estudamos os type-dependent stochastic spin models propostos por Fernández et al., os que chamaremos de modelos de spins estocástico dependentes de tipo, e que foram usados para modelar redes de sinalização biológica. A modelagem original descreve a evolução macroscópica de um modelo de spin-flip de tamanho finito com k tipos de spins, possuindo um número arbitrário de estados internos, que interagem através de uma dinâmica estocástica não reversível. No limite termodinânico foi provado que, em um intervalo de tempo finito as trajetórias convergem quase certamente para uma trajetória determinística, dada por uma equação diferencial de primeira ordem. Os comportamentos destes sistemas dinâmicos podem incluir bifurcações, relacionadas às transições de fase do modelo. O nosso objetivo principal foi de estender os modelos de spins com dinâmica de Glauber utiliza- dos pelos autores, permitindo trocas múltiplas dos spins. No contexto biológico tentamos incluir situações nas quais moléculas de tipos diferentes trocam simultaneamente os seus estados internos. Utilizando diversas técnicas, como as de grandes desvíos e acoplamento, tem sido possível demonstrar a convergência para o sistema dinâmico associado. / We study type-dependent stochastic spin models proposed by Fernández et al., which were used to model biological signaling networks. The original modeling setup describes the macroscopic evolution of a finite-size spin-flip model with k types of spins with arbitrary number of internal states interacting through a non-reversible stochastic dynamics. In the thermodynamic limit it was proved that, within arbitrary finite time-intervals, the path converges almost surely to a deterministic trajectory determined by a first-order (non-linear) differential equation. The behavior of the associated dynamical system may include bifurcations, associated to phase transitions in the statistical mechanical setting. Our aim is to extend the spin model with Glauber dynamics, to allow multiple spin-flips. In the biological context we included situations in which molecules of different types simultaneously change their internal states. Using several methods, such as large deviations and coupling, we prove the convergence theorem.

À travers une approche de contrôle optimal, cette thèse de doctorat propose une étude des modèles et des techniques de résolution dans un domaine d'application propre à la gestion du trafic aérien. Motivés par la croissance des flux aériens d'une part, et les développements en théorie du contrôle optimal d'autre part, ces travaux portent sur l'analyse du problème d'évitement de conflits aériens. Cette étude permet le développement de nouvelles approches et algorithmes en vue d'aider les contrôleurs aériens dans leur tâche. Ainsi, dans le cadre du trafic aérien, afin de préserver des distances minimales de sécurité entre avions, lors de phases tactiques et de configurations des vols en-route, notre recherche se focalise sur une stratégie de régulation subliminale en vitesse (variations très réduites), pour assurer la séparation entre avions, tout en conservant leur trajectoire prédéfinie. D'une part, une méthode de résolution numérique en contrôle optimal telle que la méthode directe de tir, impliquant une discrétisation totale ou partielle du problème, transforme le problème initial en un problème en programmation non linéaire de grande taille. Ce type de méthodes peut générer des problèmes d'optimisation de grande taille numériquement di_ciles à résoudre. Suivant le nombre de variables du problème, elles peuvent s'avérer trop coûteuse en termes de temps de calculs. D'autre part, les contraintes sur les variables d'états du problème posent des di_cultés de résolution, par exemple, pour l'usage d'une méthode numérique indirecte de tir. Développant les informations caractéristiques des conflits aériens, une détection et une détermination a priori des zones de conflits permettent alors la décomposition du problème présenté de contrôle optimal en sous-problèmes plus aisés à résoudre. La résolution des sous-problèmes hors-zones peut être abordée en utilisant les conditions du principe du maximum de Pontryagin, ce qui en permet une résolution e_cace. Une combinaison de méthodes numériques directes de tir et d'application des conditions du principe du maximum de Pontryagin est proposée, et des implémentations numériques valident ce type d'approche. / The purpose of this doctoral thesis is to study models and solution techniques based on optimal control approaches to address air tra_c management problems. Motivated by the growth of air tra_c volume, and by the advances in optimal control theory, this research works focus on analysing aircraft conflict avoidance problem. This study allows development of new approaches and algorithms to help air tra_c controllers. In the framework of air tra_c management, to ensure the minimum safety distances between aircraft, in tactical phases and en-route flight configurations, this thesis focusses on a subliminal velocity regulation strategy to perform the separation, while preserving the aircraft predefined trajectories. A numerical optimal control solution approach as the direct shooting method, wherein involves a total or partial discretization of the problem, transforms the initial problem into a large scale nonlinear programming problem. This kind of methods could generate large-size optimization problems which are numerically di_cult to solve. Depending on the number of variables which involved, this approaches could be too expensive in terms of computation time. Moreover, the state-variables constraints of the problem lead to numerical di_culties, e.g., considering the indirect numerical shooting method. Tailored on aircraft conflict avoidance problems, a detection and a determination of a priori conflict zones allow the decomposition of the optimal control problem into sub-problems, easier to solve than the original one. Solving the o_-zones sub-problems can be addressed using the Pontryagin maximum principle, which allows in this case directly the solution. A combination of direct numerical shooting method and application of conditions of Pontryagin's maximum principle is proposed, and numerical experiments validate this approach.

Neste trabalho estudamos os type-dependent stochastic spin models propostos por Fernández et al., os que chamaremos de modelos de spins estocástico dependentes de tipo, e que foram usados para modelar redes de sinalização biológica. A modelagem original descreve a evolução macroscópica de um modelo de spin-flip de tamanho finito com k tipos de spins, possuindo um número arbitrário de estados internos, que interagem através de uma dinâmica estocástica não reversível. No limite termodinânico foi provado que, em um intervalo de tempo finito as trajetórias convergem quase certamente para uma trajetória determinística, dada por uma equação diferencial de primeira ordem. Os comportamentos destes sistemas dinâmicos podem incluir bifurcações, relacionadas às transições de fase do modelo. O nosso objetivo principal foi de estender os modelos de spins com dinâmica de Glauber utiliza- dos pelos autores, permitindo trocas múltiplas dos spins. No contexto biológico tentamos incluir situações nas quais moléculas de tipos diferentes trocam simultaneamente os seus estados internos. Utilizando diversas técnicas, como as de grandes desvíos e acoplamento, tem sido possível demonstrar a convergência para o sistema dinâmico associado. / We study type-dependent stochastic spin models proposed by Fernández et al., which were used to model biological signaling networks. The original modeling setup describes the macroscopic evolution of a finite-size spin-flip model with k types of spins with arbitrary number of internal states interacting through a non-reversible stochastic dynamics. In the thermodynamic limit it was proved that, within arbitrary finite time-intervals, the path converges almost surely to a deterministic trajectory determined by a first-order (non-linear) differential equation. The behavior of the associated dynamical system may include bifurcations, associated to phase transitions in the statistical mechanical setting. Our aim is to extend the spin model with Glauber dynamics, to allow multiple spin-flips. In the biological context we included situations in which molecules of different types simultaneously change their internal states. Using several methods, such as large deviations and coupling, we prove the convergence theorem.

The focus of the thesis is on the development of a few stochastic search schemes for inverse problems and their applications in medical imaging. After the introduction in Chapter 1 that motivates and puts in perspective the work done in later chapters, the main body of the thesis may be viewed as composed of two parts: while the first part concerns the development of stochastic search algorithms for inverse problems (Chapters 2 and 3), the second part elucidates on the applicability of search schemes to inverse problems of interest in tomographic imaging (Chapters 4 and 5). The chapter-wise contributions of the thesis are summarized below. Chapter 2 proposes a Monte Carlo stochastic filtering algorithm for the recursive estimation of diffusive processes in linear/nonlinear dynamical systems that modulate the instantaneous rates of Poisson measurements. The same scheme is applicable when the set of partial and noisy measurements are of a diffusive nature. A key aspect of our development here is the filter-update scheme, derived from an ensemble approximation of the time-discretized nonlinear Kushner Stratonovich equation, that is modified to account for Poisson-type measurements. Specifically, the additive update through a gain-like correction term, empirically approximated from the innovation integral in the filtering equation, eliminates the problem of particle collapse encountered in many conventional particle filters that adopt weight-based updates. Through a few numerical demonstrations, the versatility of the proposed filter is brought forth, first with application to filtering problems with diffusive or Poisson-type measurements and then to an automatic control problem wherein the exterminations of the associated cost functional is achieved simply by an appropriate redefinition of the innovation process. The aim of one of the numerical examples in Chapter 2 is to minimize the structural response of a duffing oscillator under external forcing. We pose this problem of active control within a filtering framework wherein the goal is to estimate the control force that minimizes an appropriately chosen performance index. We employ the proposed filtering algorithm to estimate the control force and the oscillator displacements and velocities that are minimized as a result of the application of the control force. While Fig. 1 shows the time histories of the uncontrolled and controlled displacements and velocities of the oscillator, a plot of the estimated control force against the external force applied is given in Fig. 2. (a) (b) Fig. 1. A plot of the time histories of the uncontrolled and controlled (a) displacements and (b) velocities. Fig. 2. A plot of the time histories of the external force and the estimated control force Stochastic filtering, despite its numerous applications, amounts only to a directed search and is best suited for inverse problems and optimization problems with unimodal solutions. In view of general optimization problems involving multimodal objective functions with a priori unknown optima, filtering, similar to a regularized Gauss-Newton (GN) method, may only serve as a local (or quasi-local) search. In Chapter 3, therefore, we propose a stochastic search (SS) scheme that whilst maintaining the basic structure of a filtered martingale problem, also incorporates randomization techniques such as scrambling and blending, which are meant to aid in avoiding the so-called local traps. The key contribution of this chapter is the introduction of yet another technique, termed as the state space splitting (3S) which is a paradigm based on the principle of divide-and-conquer. The 3S technique, incorporated within the optimization scheme, offers a better assimilation of measurements and is found to outperform filtering in the context of quantitative photoacoustic tomography (PAT) to recover the optical absorption field from sparsely available PAT data using a bare minimum ensemble. Other than that, the proposed scheme is numerically shown to be better than or at least as good as CMA-ES (covariance matrix adaptation evolution strategies), one of the best performing optimization schemes in minimizing a set of benchmark functions. Table 1 gives the comparative performance of the proposed scheme and CMA-ES in minimizing a set of 40-dimensional functions (F1-F20), all of which have their global minimum at 0, using an ensemble size of 20. Here, 10 5 is the tolerance limit to be attained for the objective function value and MAX is the maximum number of iterations permissible to the optimization scheme to arrive at the global minimum. Table 1. Performance of the SS scheme and Chapter 4 gathers numerical and experimental evidence to support our conjecture in the previous chapters that even a quasi-local search (afforded, for instance, by the filtered martingale problem) is generally superior to a regularized GN method in solving inverse problems. Specifically, in this chapter, we solve the inverse problems of ultrasound modulated optical tomography (UMOT) and diffraction tomography (DT). In UMOT, we perform a spatially resolved recovery of the mean-squared displacements, p r of the scattering centres in a diffusive object by measuring the modulation depth in the decaying autocorrelation of the incident coherent light. This modulation is induced by the input ultrasound focussed to a specific region referred to as the region of interest (ROI) in the object. Since the ultrasound-induced displacements are a measure of the material stiffness, in principle, UMOT can be applied for the early diagnosis of cancer in soft tissues. In DT, on the other hand, we recover the real refractive index distribution, n r of an optical fiber from experimentally acquired transmitted intensity of light traversing through it. In both cases, the filtering step encoded within the optimization scheme recovers superior reconstruction images vis-à-vis the GN method in terms of quantitative accuracies. Fig. 3 gives a comparative cross-sectional plot through the centre of the reference and reconstructed p r images in UMOT when the ROI is at the centre of the object. Here, the anomaly is presented as an increase in the displacements and is at the centre of the ROI. Fig. 4 shows the comparative cross-sectional plot of the reference and reconstructed refractive index distributions, n r of the optical fiber in DT. Fig. 3. Cross-sectional plot through the center of the reference and reconstructed p r images. Fig. 4. Cross-sectional plot through the center of the reference and reconstructed n r distributions. In Chapter 5, the SS scheme is applied to our main application, viz. photoacoustic tomography (PAT) for the recovery of the absorbed energy map, the optical absorption coefficient and the chromophore concentrations in soft tissues. Nevertheless, the main contribution of this chapter is to provide a single-step method for the recovery of the optical absorption field from both simulated and experimental time-domain PAT data. A single-step direct recovery is shown to yield better reconstruction than the generally adopted two-step method for quantitative PAT. Such a quantitative reconstruction maybe converted to a functional image through a linear map. Alternatively, one could also perform a one-step recovery of the chromophore concentrations from the boundary pressure, as shown using simulated data in this chapter. Being a Monte Carlo scheme, the SS scheme is highly parallelizable and the availability of such a machine-ready inversion scheme should finally enable PAT to emerge as a clinical tool in medical diagnostics. Given below in Fig. 5 is a comparison of the optical absorption map of the Shepp-Logan phantom with the reconstruction obtained as a result of a direct (1-step) recovery. Fig. 5. The (a) exact and (b) reconstructed optical absorption maps of the Shepp-Logan phantom. The x- and y-axes are in m and the colormap is in mm-1. Chapter 6 concludes the work with a brief summary of the results obtained and suggestions for future exploration of some of the schemes and applications described in this thesis.

The neural net computer simulations which will be presented here are based on the acceptance of a set of assumptions that for the last twenty years have been expressed in the fields of information processing, neurophysiology and cognitive sciences. First of all, neural networks and their dynamical behaviors in terms of attractors is the natural way adopted by the brain to encode information. Any information item to be stored in the neural net should be coded in some way or another in one of the dynamical attractors of the brain and retrieved by stimulating the net so as to trap its dynamics in the desired item's basin of attraction. The second view shared by neural net researchers is to base the learning of the synaptic matrix on a local Hebbian mechanism. The last assumption is the presence of chaos and the benefit gained by its presence. Chaos, although very simply produced, inherently possesses an infinite amount of cyclic regimes that can be exploited for coding information. Moreover, the network randomly wanders around these unstable regimes in a spontaneous way, thus rapidly proposing alternative responses to external stimuli and being able to easily switch from one of these potential attractors to another in response to any coming stimulus.<p><p>In this thesis, it is shown experimentally that the more information is to be stored in robust cyclic attractors, the more chaos appears as a regime in the back, erratically itinerating among brief appearances of these attractors. Chaos does not appear to be the cause but the consequence of the learning. However, it appears as an helpful consequence that widens the net's encoding capacity. To learn the information to be stored, an unsupervised Hebbian learning algorithm is introduced. By leaving the semantics of the attractors to be associated with the feeding data unprescribed, promising results have been obtained in term of storing capacity. / Doctorat en sciences appliquées / info:eu-repo/semantics/nonPublished

Im Beitrag wird zunächst die konventionelle auf Signalflüssen basierte Modellbildung mit modernen leistungsflussbasierten Methoden, die auf dem Prinzip von Aktion und Reaktion aufbauen, verglichen. BG (Bond Graph), POG (Power Oriented Graph) und EMR (Energetic Macroscopic representation) sind solche modernen Methoden die den Leistungsaustausch zwischen Teilsystemen als Grundlage für den Modellbildungsansatz nutzen. Diese Werkzeuge erhalten die physikalische Struktur, erlauben es in das dynamische System hineinzuschauen und unterstützen das Verständnis des Leistungsflusses. Unterschiede werden anhand verschiedener Eigenschaften in einer Tabelle angegeben. Nach Erläuterung der Grundlagen zu POG und BG erfolgt die Vorstellung einer Freeware Zusatzbibliothek zur Simulation von Bondgraphen. Spezielle Eigenschaften werden kurz umrissen. Diese Blockbibliothek läuft unter Simulink, besteht aus nur 9 mittels Menü konfigurierbaren Blöcken und realisiert bidirektionale Verbindungen. Die Beispiele Gleichstrommotor, Pulssteller und elastische Welle demonstrieren die Vorteile der leistungsflussorientierten Modellbildung. Zustandsregelung, Energieeffizienz und Simulink LTI Analysewerkzeuge führen in die Anwendung der vorgestellten Simulink Zusatzbibliothek für Bondgraphen ein.:Modellbildung dynamischer Systeme mittels Leistungsfluß 1. Leistungsfluß versus Signalfluß 2. Konjugierte Leistungsvariablen und Kausalität 3. Grundlagen Leistungsfluß orientierter Modellierung 3.1 Definitionen zum POG (Power Oriented Graph) 3.2 Definitionen zu Grundelementen für Bondgraphen (BG) 4. Freeware Bibliothek zur Simulation von Bondgraphen 4.1 Übersicht und Nutzerfreundlichkeit 4.2 Besonderheiten 5. Beispiele 5.1 Gleichstrommotor mit starrer Welle 5.2 Elastische Welle 5.3 Eingangsfilter und Pulssteller 5.4 Vereinfachter Antriebsstrang 6. Anwendung der Simulink Bondgraph Blockbibliothek 6.1 Beispiel elastische Welle 6.2 Zustandsregelung 6.3 Energieeffizienz 6.4 Simulink Analysewerkzeuge 7. Vorteile im Überblick / The paper starts with a comparison of the conventional modelling method based on signal flow and modern power flow oriented modelling methods based on the principle of action and reaction. BG (Bond Graph), POG (Power Oriented Graph) and EMR (Energetic Macroscopic representation) are such modern methods based on the power exchange between partial systems as a key element for the basic modelling approach. These tools preserve the physical structure, enable a view inside dynamical systems and support understanding the power flow. Relationships between these graphical representations will be given. After the explanation of basics for POG and BG an overview and special features of a freeware add-on library for simulation of BGs will be outlined. The block library runs under Simulink, consists of nine menu-driven customised blocks only and realises bidirectional connections. Examples DC motor, chopper and elastic shaft demonstrate the advantages of power flow oriented modelling. State space control, energy efficiency and Simulink LTI analysis tools exemplify the application of the presented Simulink add-on BG library.:Modellbildung dynamischer Systeme mittels Leistungsfluß 1. Leistungsfluß versus Signalfluß 2. Konjugierte Leistungsvariablen und Kausalität 3. Grundlagen Leistungsfluß orientierter Modellierung 3.1 Definitionen zum POG (Power Oriented Graph) 3.2 Definitionen zu Grundelementen für Bondgraphen (BG) 4. Freeware Bibliothek zur Simulation von Bondgraphen 4.1 Übersicht und Nutzerfreundlichkeit 4.2 Besonderheiten 5. Beispiele 5.1 Gleichstrommotor mit starrer Welle 5.2 Elastische Welle 5.3 Eingangsfilter und Pulssteller 5.4 Vereinfachter Antriebsstrang 6. Anwendung der Simulink Bondgraph Blockbibliothek 6.1 Beispiel elastische Welle 6.2 Zustandsregelung 6.3 Energieeffizienz 6.4 Simulink Analysewerkzeuge 7. Vorteile im Überblick

En aquest treball s'ha estudiat la dinàmica dels làsers de classe A i de classe B en termes del potencial de Lyapunov. En el cas que s'injecti un senyal al làser o es modulin alguns dels paràmetres, apareix un comportament moltmés complex i s'estudia el conjunt de bifurcacions.1) Als làsers de classe A, la dinàmica determinista s'ha interpretat com el moviment damunt el potencial de Lyapunov. En la dinàmica estocàstica s'obté un flux sostingut per renou per a la fase del camp elèctric.2) Per als làsers de classe A amb senyal injectat, s'ha descrit el conjunt de bifurcacions complet i s'ha determinat el conjunt d'amplituds i freqüències en el quals el làser responajustant la seva freqüència a la del camp extern. 3) S'ha obtingut un potencial de Lyapunov pels làsers de classe B, només vàlid en el cas determinista, que inclou els termes de saturació de guany i d'emissió espontània.4) S'ha realitzat un estudi del conjunt de bifurcacions parcial al voltant del règim tipus II de la singularitat Hopf--sella--node en un làser de classe B amb senyal injectat.5) S'han identificat les respostes òptimes pels làsers de semiconductor sotmesos a modulació periòdica externa. S'han obtingut les corbes que donen la resposta màxima per cada tipus de resonància en el pla definit per l'amplitud relativa de modulació i la freqüència de modulació. / In this work we have studied the dynamics of both class A and class B lasers in terms of Lyapunov potentials. In the case of an injected signal or when some laser parameters are modulated, and more complex behaviour is expected, the bifurcation set is studied. The main results are the following:1) For class A lasers, the deterministic dynamics has been interpreted as a movement on the potential landscape. In the stochastic dynamics we have found a noise sustained flow for the phase of the electric field. 2) For class A lasers with an injected signal, we have been able to describe the whole bifurcation set of this system and to determine the set of amplitudes frequencies for which the laser responds adjusting its frequency to that of the external field. 3) In the case of class B lasers, we have obtained a Lyapunov potential only valid in the deterministic case, including spontaneous emission and gain saturation terms. The fixed point corresponding to the laser in the on state has been interpreted as a minimum in this potential. Relaxation to this minimum is reached through damped oscillations. 4) We have performed a study of the partial bifurcation set around the type II regime of the Hopf-saddle-node singularity in a class B laser with injected signal. 5) We have identified the optimal responses of a semiconductor laser subjected to an external periodic modulation. The lines that give a maximum response for each type of resonance are obtained in the plane defined by the relative amplitude modulation and frequency modulation.

Dizertační práce se zabývá elektronicky nastavitelnými oscilátory, studiem nelineárních vlastností spojených s použitými aktivními prvky a posouzením možnosti vzniku chaotického signálu v harmonických oscilátorech. Jednotlivé příklady vzniku podivných atraktorů jsou detailně diskutovány. V doktorské práci je dále prezentováno modelování reálných fyzikálních a biologických systémů vykazujících chaotické chování pomocí analogových elektronických obvodů a moderních aktivních prvků (OTA, MO-OTA, CCII ±, DVCC ±, atd.), včetně experimentálního ověření navržených struktur. Další část práce se zabývá možnostmi v oblasti analogově – digitální syntézy nelineárních dynamických systémů, studiem změny matematických modelů a odpovídajícím řešením. Na závěr je uvedena analýza vlivu a dopadu parazitních vlastností aktivních prvků z hlediska kvalitativních změn v globálním dynamickém chování jednotlivých systémů s možností zániku chaosu v důsledku parazitních vlastností použitých aktivních prvků.