Nichtlineare multistabile Systeme unter dem Einfluss von Rauschen weisen vielschichtige dynamische Eigenschaften auf. <br /> Ein mittleres Rauschlevel zeitigt ein Springen zwischen den metastabilen Zustaenden. <br /> Dieser “attractor-hopping” Prozess ist gekennzeichnet durch laminare Bewegung in der Naehe von Attraktoren und erratische Bewegung, die sich auf chaotischen Satteln abspielt, welche in die fraktalen Einzugsgebietsgrenzen eingebettet sind. Er hat rauschinduziertes Chaos zur Folge. <br /> Bei der Untersuchung der dissipativen Standardabbildung wurde das Phaenomen der Praeferenz von Attraktoren durch die Wirkung des Rauschens gefunden. Dies bedeutet, dass einige Attraktoren eine groessere Wahrscheinlichkeit erhalten aufzutreten, als dies fuer das rauschfreie System der Fall waere. Bei einer bestimmten Rauschstaerke ist diese Bevorzugung maximal. <br /> Andere Attraktoren werden aufgrund des Rauschens weniger oft angelaufen. Bei einer entsprechend hohen Rauschstaerke werden sie komplett ausgeloescht. <br /> Die Komplexitaet des Sprungprozesses wird fuer das Modell zweier gekoppelter logistischer Abbildungen mit symbolischer Dynamik untersucht. <br /> Bei Variation eines Parameters steigt an einem bestimmten Wert des Parameters die topologische Entropie steil an, die neben der Shannon Entropie als Komplexitaetsmass verwendet wird. Dieser Anstieg wird auf eine neuartige Bifurkation von chaotischen Satteln zurueckgefuehrt, die in einem Verschmelzen zweier Sattel besteht und durch einen “Snap-back”-Repellor vermittelt wird. <br /> Skalierungsgesetze sowohl der Verweilzeit auf einem der zuvor getrennten Teile des Sattels als auch des Wachsens der fraktalen Dimension des entstandenen Sattels beschreiben diese neuartige Bifurkation genauer. <br /> Wenn ein chaotischer Sattel eingebettet in der offenen Umgebung eines Einzugsgebietes eines metastabilen Zustandes liegt, fuehrt das zu einer deutlichen Senkung der Schwelle des rauschinduzierten Tunnelns. <br /> Dies wird anhand der Ikeda-Abbildung, die ein Lasersystem mit einer zeitverzoegerden Interferenz beschreibt, demonstriert. Dieses Resultat wird unter Verwendung der Theorie der Quasipotentiale erzielt. <br /> Sowohl dieser Effekt, die Senkung der Schwelle für rauschinduziertes Tunneln aus einem metastabilen Zustand durch einen chaotischen Sattel, als auch die beiden Skalierungsgesteze sind von experimenteller Relevanz. / Nonlinear multistable systems under the influence of noise exhibit a plethora of interesting dynamical properties. A medium noise level causes hopping between the metastable states. This attractorhopping process is characterized through laminar motion in the vicinity of the attractors and erratic motion taking place on chaotic saddles, which are embedded in the fractal basin boundary. This leads to noise-induced chaos. The investigation of the dissipative standard map showed the phenomenon of preference of attractors through the noise. It means, that some attractors get a larger probability of occurrence than in the noisefree system. For a certain noise level this prefernce achieves a maximum. Other attractors are occur less often. For sufficiently high noise they are completely extinguished. The complexity of the hopping process is examined for a model of two coupled logistic maps employing symbolic dynamics. With the variation of a parameter the topological entropy, which is used together with the Shannon entropy as a measure of complexity, rises sharply at a certain value. This increase is explained by a novel saddle merging bifurcation, which is mediated by a snapback repellor. Scaling laws of the average time spend on one of the formerly disconnected parts and of the fractal dimension of the connected saddle describe this bifurcation in more detail. If a chaotic saddle is embedded in the open neighborhood of the basin of attraction of a metastable state, the required escape energy is lowered. This enhancement of noise-induced escape is demonstrated for the Ikeda map, which models a laser system with time-delayed feedback. The result is gained using the theory of quasipotentials. This effect, as well as the two scaling laws for the saddle merging bifurcation, are of experimental relevance.

Die vorliegende Arbeit umfasst die Entwicklung eines Rahmens zur Bewertung der Stabilität von (multistabilen) komplexen (vernetzten) dynamischen Systemen. Als ersten Beitrag schlagen wir die multiple-node basin stability (MNBS) vor, um die Stabilität vernetzter dynamischer Systeme als Reaktion auf nicht-infinitesimale Störungen zu messen, die gleichzeitig mehrere Knoten des Systems beeinflussen. Weiterhin beziehen wir uns auf das Konzept der Resilienz zur Charakterisierung von Multistabilität. Inspiriert vom Konzept der ökologischen Resilienz schlussfolgern wir, dass die Stabilität der verschiedenen Attraktoren eines multistabilen Systems von der Gesamtstruktur ihrer jeweiligen Einzugsgebiet bestimmt wird. Insbesondere identifizieren wir sowohl die lokale Dynamik des Systems im Zustandsraum als auch die relative Position des Attraktors im Einzugsgebiet zusätzlich zum dessen Volumen als entscheidende Aspekte, welche die Gesamtstabilität eines Attraktors charakterisieren. Die genannten Aspekte werden im Maß der integral stability (IS) für die ganzheitliche Quantifizierung von Multistabilität zusammengeführt. Komplementär lässt sich auch das Konzept der technischen Resilienz betrachten, welches sich auf die Rückkehrgeschwindigkeit eines Systems zu seinem Gleichgewicht, in Folge einer Störung, bezieht. Im spezifischen Kontext von vernetzten dynamischen Systemen definieren wir die single-node recovery time (SNRT). Diese stellt ein neues Maß zur Schätzung der relativen Zeitskalen dar, die der transienten Knotendynamik eines Netzwerks zugrunde liegen, welches nach einer nicht-infinitesimalen Störung an einem Knoten in seinen gewünschten Betriebszustand zurückkehrt. Schliesslich befassen wir uns mit der Untersuchung der Synchronisationsstabilität in speziellen komplexen Netzwerken, welche entweder die Kleine-Welt-Eigenschaft aufweisen oder eine Kombination aus skalenfreier Knotengradverteilung und hierarchischer Organisation zeigen. / The present endeavour comprises the development of a framework for the assessment of the stability of (multistable) complex (networked) dynamical systems. As a first contribution, we propose the framework of multiple-node basin stability (MNBS) for gauging the stability of networked dynamical systems in response to non-infinitesimal perturbations simultaneously affecting multiple nodes of the system. We then turn to the theoretical framework of resilience in identifying the different aspects characterizing multistability. Inspired by the concept of ecological resilience, we assert that the stability of the different attractors of a multistable system is determined by the overall structure of their respective basins of attraction. In particular, we identify the local dynamics of the system in the state space and the relative position of the attractor within the basin, in addition to the volume of the basin of attraction as crucial aspects determining overall stability of an attractor. We combine the aforementioned aspects in proposing the measure of integral stability (IS) for holistically quantifying multistability. We also draw inspiration from the concept of engineering resilience, which relates to the speed of return of the system to its equilibrium, following a perturbation. In the specific context of networked dynamical systems, we propose the framework of single-node recovery time (SNRT) for obtaining an estimate of the relative time scales underlying the transient dynamics of the nodes of a network returning to its desired operational state, following a non-infinitesimal perturbation to any specific node. Finally, we delve into the explicit investigation of the stability of synchronization on complex dynamical networks exhibiting small-world properties and of those, simultaneously displaying scale-free behaviour and hierarchical organization.

In dieser Arbeit werden zwei nichtlineare Phänomene untersucht, Multistabilität durch verzögerte Rückkopplung und Synchronisation von quasiperiodischen Oszillationen. Dies geschieht mit Hilfe von Halbleiterlasern und auf dem selben Chip wie der Laser integrierter ultrakurzer optischer Rückkopplung. Verzögerte Rückkopplung ist unter anderem die Ursache für das Phänomen der Faltung von Lasermoden, und damit für das Auftreten von mehreren möglichen Laserzuständen für die selben Parameter. Ein tristabiles Regime von Dauerstrichzuständen kann im Experiment für mehrere breite Parameterbereiche der Rückkopplung beobachtet werden. Sehr nahe der Laserschwelle wird einer der Laserzustände durch den stabilen ``aus''''-Zustand ersetzt. Theoretische Betrachtungen im Rahmen des paradigmatischen Lang-Kobayashi Models verzögerter Rückkopplung ermöglichen eine in sich konsistente Interpretation der experimentellen Ergebnisse. Neben der Beeinflussung des stationären Verhaltens eines Halbleiterlasers kann verzögerte Rückkopplung Instabilitäten in der Laseremission hervorrufen. Abhängig von Rückkoppelstärke und -phase werden zwei verschiedene Intensitätspulsationen des emittierten Lichtes beobachtet. Synchronisationsprozesse solcher Pulsationen wurden von mir in einem System von zwei verschiedenen gekoppelten Multisektionslasern untersucht. Periodische Selbstpulsationen von Laser 1 werden hierfür in Laser 2 injiziert, welcher sich in einem Regime quasiperiodischer Intentensitätspulsationen mit zwei fundamentalen Frequenzen befindet. Das Experiment zeigt eine neue Art von Übergang zu synchronem Verhalten, welche kürzlich mit Hilfe von gekoppelten generischen Phasen- und van der Pol Oszillatormodellen aufgedeckt wurde. Desweiteren konnten bislang unerforschte Prozesse des Kohärenzübertrags auch zu nichtsynchronisierten Oszillationen beobachtet werden. / In this work two nonlinear phenomena are investigated, multistability due to delayed feedback and synchronization of quasiperiodic oscillations. The experimental devices are semiconductor lasers with ultra-short optical feedback, which is integrated on the same chip as the laser. Delayed feedback causes the folding of lasing modes, leading to hysteresis effects and even the coexistence of several laser states for the same parameters. A regime of tristability of continuous-wave (cw) states is found for multiple ranges of applied currents. Very close to threshold, one of the lasing states may be replaced by the stable ``off''''-state. Theoretical investigations in the framework of the paradigmatic Lang-Kobayashi model provide a consistent understanding of the experimental findings. Besides modifying the stationary behavior of a semiconductor laser, delayed feedback can cause instabilities of the laser output. Depending on strength and phase of the feedback, two types of self-sustaining pulsations of the emitted light intensity are found in our devices. Synchronization processes of such pulsations are studied in a system of two coupled multisection lasers. Periodic self-pulsations of laser 1 are injected into laser 2, which is operating in a regime with two-frequency quasiperiodic self-pulsations. The experimental system demonstrates the new type of transitions to synchrony between three frequencies which has been recently revealed using generic coupled phase and van der Pol oscillator models. Moreover, carefully determining the coherence of the noisy oscillations, so far unexplored processes of coherence transfer to nonsynchronized oscillations are revealed.

A natural auditory scene contains many sound sources each of which produces complex sounds. These sounds overlap and reach our ears at the same time, but they also change constantly. To still be able to follow the sound source of interest, the auditory system must decide where each individual tone belongs to and integrate this information over time. For well-controlled investigations on the mechanisms behind this challenging task, sound sources need to be simulated in the lab. This is mostly done with sine tones arranged in certain spectrotemporal patterns. The vast majority of studies simply interleave two sub-sequences of sine tones. Participants report how they perceive these sequences or they perform a task whose performance measure allows hints on how the scene was perceived. While many important insights have been gained with this procedure, the questions that can be addressed with it are limited and the commonly used response methods are partly susceptible to distortions or only indirect measures. The present thesis enlarged the complexity of the tone sequences and the diversity of perceptual measures used for investigations on auditory scene analysis. These changes are intended to open up new questions and give new perspectives on our knowledge about auditory scene analysis. In detail, the thesis established three-tone sequences as a tool for specific investigations on the perceptual foreground and background processing in complex auditory scenes. In addition, it modifies an already established approach for indirect measures of auditory perception in a way that enables detailed and univocal investigations on background processing. Finally, a new response method, namely a no-report method for auditory perception that might also serve as a method to validate subjective report measures, was developed. This new methodological approach uses eye movements as a measurement tool for auditory perception. With the aid of all these methodological improvements, the current thesis shows that auditory foreground formation is actually more complex than previously assumed since listeners hold more than one auditory source in the foreground without being forced to do so. In addition, it shows that the auditory system prefers a limited number of specific source configurations probably to avoid combinatorial explosion. Finally, the thesis indicates that the formation of the perceptual background is also quite complex since the auditory system holds perceptual organization alternatives in parallel that were basically assumed to be mutually exclusive. Thus, both the foreground and the background follow different rules than expected based on two-tone sequences. However, one finding seems to be true for both kinds of sequences: the impact of the tone pattern on the subjective perception is marginal, be it in two- or three-tone sequences. Regarding the no-report method for auditory perception, the thesis shows that eye movements and the reported auditory foreground formations were in good agreement and it seems like this approach indeed has the potential to become a first no-report measure for auditory perception.:Abstract 3 Acknowledgments 5 List of Figures 8 List of Tables 9 Collaborations 11 1 General Introduction 13 1.1 The auditory foreground 13 1.1.1 Attention and auditory scene analysis 13 1.1.2 Investigating auditory scene analysis with two-tone sequences 16 1.1.3 Multistability 18 1.2 The auditory background 21 1.2.1 Investigating auditory background processing 22 1.3 Measures of auditory perception 23 1.3.1 Report procedures 23 1.3.2 Performance-based measures 26 1.3.3 Psychophysiological measures 27 1.4 Summary and goals of the thesis 30 2 The auditory foreground 33 2.1 Study 1: Foreground formation in three-tone sequences 33 2.1.1 Abstract 33 2.1.2 Introduction 33 2.1.3 Methods 37 2.1.4 Results 43 2.1.5 Discussion 48 2.2 Study 2: Pattern effects in three-tone sequences 53 2.2.1 Abstract 53 2.2.2 Methods 53 2.2.3 Results 54 2.2.4 Discussion 58 2.3 Study 3: Pattern effects in two-tone sequences 59 2.3.1 Abstract 59 2.3.2 Introduction 59 2.3.3 General Methods 63 2.3.4 Experiment 1 – Methods and Results 65 2.3.5 Experiment 2 – Methods and Results 67 2.3.6 Experiment 3 – Methods and Results 70 2.3.7 Discussion 72 3 The auditory background 74 3.1 Study 4: Background formation in three-tone sequences 74 3.1.1 Abstract 74 3.1.2 Introduction 74 3.1.3 Methods 77 3.1.4 Results 82 3.1.5 Discussion 86 4 Audio-visual coupling for investigations on auditory perception 90 4.1 Study 5: Using Binocular Rivalry to tag auditory perception 90 4.1.1 Abstract 90 4.1.2 Introduction 90 4.1.3 Methods 92 4.1.4 Results 100 4.1.5 Discussion 108 5 General Discussion 113 5.1 Short review of the findings 113 5.2 The auditory foreground 114 5.2.1 Auditory foreground formation and attention theories 114 5.2.2 The role of tone pattern in foreground formation 116 5.2.3 Methodological considerations and continuation 117 5.3 The auditory background 118 5.3.1 Auditory object formation without attention 120 5.3.2 Multistability without attention 121 5.3.3 Methodological considerations and continuation 122 5.4 Auditory scene analysis by audio-visual coupling 124 5.4.1 Methodological considerations and continuation 124 5.5 Artificial listening situations and conclusions on natural hearing 126 6 Conclusions 128 References 130

Perceptual multistability is a phenomenon that is mostly studied in all modalities separately. The phenomenon reveals fundamental principles of the perceptual system in the formation of an emerging cognitive representation in the consciousness. The momentary perceptual organizations evoked during the stimulation with ambiguous stimuli switches between several perceptual organizations or percepts: The auditory streaming stimulus in audition and the moving plaids stimulus in vision, elicit different at least two percepts that dominate awareness exclusively for a random phase or dominance duration before an inevitable switch to another percept occurs. The similarity in the perceptual experience has led to propose a global mechanism contributing to the perceptual multistability phenomena crossmodally. Contrary, the difference in the perceptual experience has led to propose a distributed mechanism that is modality-specific. The development of a hybrid model has synergized both approaches. We accumulate empirical evidence for the contribution of a global mechanism, albeit distributed mechanisms play an indispensable role in this cross-modal interplay. The overt report of the perceptual experience in our experiments is accompanied by the recording of objective, cognitive markers of the consciousness: Reflexive movements of the eyes, namely the dilation of the pupil and the optokinetic nystagmus, correlate with the unobservable perceptual switches and perceptual states respectively and have their neuronal rooting in the brainstem. We complement earlier findings on the sensitivity of the pupil to visual multistability: It was shown in two independent experiments that the pupil dilates at the time of reported perceptual switches in auditory multistability. A control condition on confounding effects from the reporting process confines the results. Endogenous, evoked internally by the unchanged stimulus ambiguity, and exogenous, evoked externally by the changes in the physical properties of the stimulus, perceptual switches could be discriminated based on the maximal amplitude of the dilation. The effect of exogenous perceptual has on the pupil were captured in a report and no-report task to detect confounding perceptual effects. In two additional studies, the moment-by-moment coupling and coupling properties of percepts between concurrent multistable processes in audition, evoked by auditory streaming, and in vision, evoked by moving plaids, were found crossmodally. In the last study, the externally induced percept in the visual multistable process was not relayed to the simultaneous auditory multistable process: Still, the observed general coupling is fragile but existent. The requirement for the investigation of a moment-by-moment coupling of the multistable perceptual processes was the application of a no-report paradigm in vision: The visual stimulus evokes an optokinetic nystagmus that has machine learnable different properties when following either of the two percepts. In combination with the manually reported auditory percept, attentional bottlenecks due to a parallel report were circumvented. The two main findings, the dilation of the pupil along reported auditory perceptual switches and the crossmodal coupling of percepts in bimodal audiovisual multistability, speak in favor of a partly global mechanism being involved in control of perceptual multistability; the global mechanism is incarcerated by the, partly independent, distributed competition of percepts on modality level. Potentially, supramodal attention-related modulations consolidate the outcome of locally distributed perceptual competition in all modalities.:COVER 1 BIBLIOGRAPHISCHE BESCHREIBUNG 2 ACKNOWLEDGEMENTS 3 CONTENTS 4 CHAPTER 1: Introduction 6 C1.1: Stability and uncertainty in perception 6 C1.2: Auditory, visual and audio-visual multistability 14 C1.3: Capturing the subjective perceptual experience 25 C1.4: Limitations of preceding studies, objectives, and outline of the Thesis 33 CHAPTER 2: Study 1 “Pupillometry in auditory multistability” 36 C2.1.1 Experiment 1: Introduction 36 C2.1.2 Experiment 1: Material and Methods 38 C2.1.3 Experiment 1: Data analysis 44 C2.1.4 Experiment 1: Results 48 C2.1.5 Experiment 1: Discussion 52 C2.2.1 Experiment 2: Introduction 54 C2.2.2 Experiment 2: Material and Methods 54 C2.2.3 Experiment 2: Data analysis 56 C2.2.4 Experiment 2: Results 57 C2.3 Experiment 1 & 2: Discussion 61 C2.4 Supplement Study 1 65 CHAPTER 3: Study 2 “Multimodal moment-by-moment coupling in perceptual bistability” 71 C3.1.1 Experiment 1: Introduction 71 C3.1.2 Experiment 1: Results 74 C3.1.3 Experiment 1: Discussion 80 C3.1.4 Experiment 1: Material and Methods 84 C3.1.5 Experiment 1: Data analysis 87 C3.2 Supplement Study 2 92 CHAPTER 4: Study 3 “Boundaries of bimodal coupling in perceptual bistability” 93 C4.1.1 Experiment 1: Introduction 93 C4.1.2 Experiment 1: Material and Methods 98 C4.1.3 Experiment 1: Data analysis 102 C4.1.4 Experiment 1: Results 108 C4.1.5 Experiment 1: Discussion 114 C4.2.1 Experiment 2: Introduction 116 C4.2.2 Experiment 2: Material and Methods 119 C4.2.3 Experiment 2: Data analysis 125 C4.2.4 Experiment 2: Results 133 C4.3 Experiment 1 & 2: Discussion 144 C4.4 Supplement Study 3 151 CHAPTER 5: General Discussion 154 C5.1 Significance for models of multistability and implications for the perceptual architecture 162 C5.2 Recommendations for future research 166 C5.3 Conclusion 168 REFERENCES 170 APPENDIX 186 A1: List of Figures 186 A2: List of Tables 188 A3: List of Abbreviations and Symbols 189

Magnetic Shape Memory (MSM) alloys show a superelastic behaviour with possible deformation rates up to 6% until 12% and a sufficient lifetime performance [1, 2]. In this paper, a passive application for a superelastic Ni-Mn-Ga-alloy is presented by using the MSM element as an accurately defined inner friction in a system of a multistable actuator, in particular a multistable proportional valve. The multistable valve is characterized by a currentless holding of the valve displacement in any position of the stroke. This circumstance makes the concept a very low energy consumption valve, compared to conventional proportional valves with solenoid actuators. The new aspect of a rigid connection of MSM Materials enables an absorption of tension as well as compressive forces. To realize an applicable controlling valve, a simple and effective controlling strategy has been implemented. Due to the stabilizing effect of the MSM element, an accurate controlling of the valve stroke and the usage for example as a pressure-, mass-flow or temperature-controlling valve was made possible. Furthermore, some potential applications in pneumatics as well as in hydraulics are presented.

Sensory inputs can be ambiguous. A physically constant stimulus that induces several perceptual alternatives is called multistable. Many factors can influence perception. In this thesis I investigate factors that affect visual multistability. All presented studies use a pattern-component rivalry stimulus consisting of two gratings drifting in opposite directions (called the plaid stimulus). This induces an “integrated” perception of a moving plaid (the pattern) or a “segregated” perception of overlaid gratings (the components). One study (chapter 2) investigates parameter dependence of a plaid stimulus on perception, with particular emphasis on the first percept. Specifically, it addresses how the enclosed angle (opening angle) affects the perception at stimulus onset and during prolonged viewing. The effects that are shown persist even if the stimulus is rotated. On a more abstract level it is shown that percepts can influence each other over time (chapter 3) which emphasizes the importance of instructions and report mode. In particular, it relates to the decision which percepts are instructed to be reported at all as well as which percepts can be reported as separate entities and which are pooled into the same response option. A further abstract level (predictability of a stimulus change, chapter 5) shows that transferring effects from one modality to another modality (specifically from audition to vision) requires careful choice of stimulus parameters. In this context, we give considerations to the proposal for a wider usage of sequential stopping rules (SSR, chapter 4), especially in studies where effect sizes are hard to estimate a priori. This thesis contributes to the field of visual multistability by providing novel experimental insights into pattern-component rivalry and by linking these findings to data on sequential dependencies, to the optimization of experimental designs, and to models and results from another sensory modality.:Bibliographische Beschreibung 3 Acknowledgments 4 CONTENTS 5 Collaborations 7 List of Figures 8 List of Tables 8 1. Introduction 9 1.1. Tristability 10 1.2. Two or more interpretations? 11 1.3. Multistability in different modalities 12 1.3.1. Auditory multistability 12 1.3.2. Haptic multistability 13 1.3.3. Olfactory multistability 13 1.4. multistability with several interpretations 13 1.5. Measuring multistability 14 1.5.1. The optokinetic nystagmus 14 1.5.2. Pupillometry 15 1.5.3. Measuring auditory multistability 15 1.5.4. Crossmodal multistability 16 1.6. Factors governing multistability 16 1.6.1. Manipulations that do not involve the stimulus 16 1.6.2. Manipulation of the stimulus 17 1.6.2.1. Factors affecting the plaid stimulus 17 1.6.2.2. Factors affecting the auditory streaming stimulus 18 1.7. Goals of this thesis 18 1.7.1. Overview of the thesis 18 2. Parameter dependence in visual pattern-component rivalry at onset and during prolonged viewing 21 2.1. Introduction 21 2.2. Methods 24 2.2.1. Participants 24 2.2.2. Setup 24 2.2.3. Stimuli 25 2.2.4. Procedure 26 2.2.5. Analysis 27 2.2.6. (Generalized) linear mixed-effects models 30 2.3. Results 30 2.3.1. Experiment 1 30 2.3.1.1. Relative number of integrated percepts 31 2.3.1.2. Generalized linear mixed-effects model 32 2.3.1.3. Dominance durations 33 2.3.1.4. Linear mixed-effects models 33 2.3.1.5. Control: Disambiguated trials 33 2.3.1.6. Time course of percept reports at onset 34 2.3.1.7. Eye movements 35 2.3.2. Experiment 2 36 2.3.2.1. Relative number of percepts 36 2.3.2.2. Generalized linear mixed-effects model 37 2.3.2.3. Dominance durations 38 2.3.2.4. Linear mixed-effects model 38 2.3.2.5. Control: Disambiguated trials 40 2.3.2.6. Time course of percept reports at onset 42 2.3.2.7. Eye movements 44 2.4. Discussion 45 2.5. Appendix 49 2.5.1. Appendix A 49 3. Perceptual history 51 3.1. Markov chains 52 3.1.1. Markov chains of order 1 and 2 52 3.2. Testing for Markov chains 55 3.2.1. The method of Naber and colleagues (2010) 56 3.2.1.1. The method 56 3.2.1.2. Advantages and disadvantages of the method 56 3.2.2. Further methods for testing Markov chains 57 3.3. Summary and discussion 58 4. Sequential stopping rules 60 4.1. The COAST rule 61 4.2. The CLAST rule 61 4.3. The variable criteria sequential stopping rule 61 4.4. Discussion 62 4.5. Using the vcSSR when transferring an effect from audition to vision 64 5. Predictability in visual multistability 66 5.1. Pretests 66 5.2. Predictability effects in visual pattern-component rivalry 69 5.2.1. Introduction 69 5.2.2. Methods 71 5.2.2.1. Participants 71 5.2.2.2. Setup 72 5.2.2.3. Stimuli 73 5.2.2.4. Conditions 73 5.2.2.5. Design and procedure 73 5.2.2.6. Analysis 74 5.2.3. Results 75 5.2.3.1. Valid reports 75 5.2.3.2. Verification of reports by eye movements 76 5.2.3.3. Onset latency 76 5.2.3.4. Dominance durations 78 5.2.3.5. Relative dominance of the segregated percept 78 5.2.4. Discussion 78 6. General discussion 83 6.1. Reporting percepts 83 6.1.1. Providing two versus three response options 83 6.1.2. Stimuli with more than three percepts 84 6.1.3. When to pool percepts together and when not 84 6.1.4. Leaving out percepts 87 6.1.5. Measuring (unreported) percepts 88 6.2. Comparing influencing factors on different levels 88 6.3. The use of the vcSSR 90 6.4. Valid reports 90 6.5. Conclusion 93 References 94