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Abstract This paper presents a new four-dimensional (4-D) smooth quadratic autonomous chaotic system, which can present periodic orbit, chaos, and hyperchaos under the conditions on different parameters. Importantly, the system can generate a four-wing hyper-chaotic attractor and a pair of coexistent doublewing hyper-chaotic attractors with two symmetrical initial conditions. Furthermore, a four-wing transient chaos occurs in the system. The dynamic analysis approach- in the paper involves time series, phase portraits, Poincaré maps, bifurcation diagrams, and Lyapunov exponents, to investigate some basic dynamical behaviors of the proposed 4-D system.

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by Law Chi Kwong. / Parallel title in Chinese characters. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1989. / Bibliography: leaves 73-75. / by Law Chi Kwong.

Chan Chung Ning. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves [86]-88). / Text in English; abstracts in English and Chinese. / Chan Chung Ning. / Abstract --- p.i / Abstract in Chinese --- p.ii / Acknowledgement --- p.iii / Contents --- p.iv / List of Figures --- p.vii / List of Tables --- p.xi / Chapter Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- Classical chaos and quantum chaos --- p.1 / Chapter 1.2 --- Motivations --- p.2 / Chapter 1.3 --- Structure of our study --- p.3 / Chapter Chapter 2. --- Integrability of Hamiltonian Systems --- p.5 / Chapter 2.1 --- Integrable systems --- p.5 / Chapter 2.2 --- KAM perturbation and Poincare surface section --- p.8 / Chapter 2.3 --- Surface sections of Robnik Billiards --- p.11 / Chapter 2.4 --- Linking classical and quantum chaos --- p.16 / Chapter Chapter 3. --- Constraint Operator Method --- p.18 / Chapter 3.1 --- Two-dimensional billiards --- p.18 / Chapter 3.2 --- Formalism of the constraint operator method with the Dirichlet boundary conditions --- p.19 / Chapter 3.3 --- Numerical results: eigenvalues of billiards --- p.24 / Chapter 3.4 --- Discussion on the constraint operator method --- p.29 / Chapter Chapter 4. --- The COM with the Neumann Boundary Conditions --- p.32 / Chapter 4.1 --- Formalism --- p.32 / Chapter 4.2 --- Numerical results --- p.35 / Chapter 4.3 --- Discussion --- p.38 / Chapter Chapter 5. --- Boundary Integral Method --- p.40 / Chapter 5.1 --- Introduction --- p.40 / Chapter 5.2 --- Berry's formalism --- p.41 / Chapter 5.3 --- A modified formalism --- p.46 / Chapter 5.4 --- Numerical results --- p.47 / Chapter 5.5 --- Discussion on the BIM --- p.53 / Chapter Chapter 6. --- Further Discussions on the BIM --- p.55 / Chapter 6.1 --- The choice of the Green's function --- p.55 / Chapter 6.2 --- Principal value --- p.58 / Chapter Chapter 7. --- Conformal Mapping Method --- p.64 / Chapter 7.1 --- Formalism --- p.64 / Chapter 7.2 --- Numerical results --- p.69 / Chapter 7.3 --- Summary --- p.73 / Chapter Chapter 8. --- Spectral Statistics --- p.76 / Chapter 8.1 --- Introduction --- p.76 / Chapter 8.2 --- Numerical results --- p.78 / Chapter 8.3 --- Summary --- p.80 / Chapter Chapter 9. --- Conclusion --- p.83 / Bibliography --- p.86

This paper investigates the complex systems and the dynamical behaviors in disordered-coupled random Boolean networks. In first part, we give a simple introduction to Kauffman¡¦s network and cellular automata, and apply them to study the virus dynamics and spatial distribution of ant lions. In the second part, a disordered coupling mechanism is introduced to study the dynamical behaviors (especially the synchronization phenomena) of random Boolean networks. Though the interactions between networks are microscopic, we formulate a macroscopic coupled model to describe the dynamics of the original system. The model tallies well with the original system. When the coupling strength exceeds the critical value, the coupling is sufficient to overcome the divergent nature of non-linearity and mutual synchronization is achieved. The finite size effect and different coupling configuration are also under our discussion.

Thèse de docteur-ingénieur : Génie civil : Villeurbanne, INSA : 2001. / Thèse : 2001ISAL0033. Titre provenant de l'écran-titre. Bibliogr. p.251-264.

Mémoire (M.A.)--Université du Québec à Chicoutimi, 1997. / Document électronique également accessible en format PDF. CaQCU

In this project Rayleigh Bénard convection (RBC) in a cylindrical domain with experimentally realistic boundaries was investigated numerically. The results were obtained using large-scale parallel calculations. The flow field was determined as well as its linearized solutions in order to obtain Lyapunov diagnostics. The emphasis is on the effects that the domain size Γ (gamma) has on the system dynamics (Γ = radius/depth for a cylindrical domain). Temperature fields were viewed for different Γ's) and a transition to spiral defect chaos was observed for large Γ's. The temperature and thermal perturbation fields were inspected for Γ = 10 and large perturbations were found to be very localized and caused by small defects in the temperature field. The azimuthal average of thermal perturbations indicate that the perturbations are largest at the boundaries for small domains and largest at the center for large domains. This suggests that small to intermediate aspect ratio RBC should not be thought of as a set of weakly correlated regions in space. The leading order Lyapunov exponent was positive over a range of conditions indicating that the system is truly chaotic. The fractal dimension was calculated for several domain sizes and the system was found to be extensive even though the system dynamics change significantly. / Master of Science