Analysis of Complex Nonlinear Dynamical Systems

The aim of this book is to introduce and study some chaotic and hyperchaotic complex nonlinear systems. Basic properties of these systems including symmetry, dissipation and stability of the equilibrium points are analyzed. The dynamics of these systems is rich in the sense that our systems exhibit chaotic, hyperchaotic attractors, periodic, quasi-periodic solutions and solutions that approach fixed points. Numerically the range of parameters values of the system at which hyperchaotic attractors exist is calculated based on the calculations of Lyapunov exponents. The signs of Lyapunov exponents provide a good classification of these systems. The dynamics of these systems is also studied by calculating its bifurcation diagrams. A circuit diagram is designed for one of hyperchaotic complex systems in chapter 5 and simulated using Matlab/Simulink to verify the hyperchaotic behavior. The problem of chaos and hyperchaos control is treated by adding the complex periodic forcing. The control performances are verified by calculating Lyapunov exponents.