Complexity Studies in Some Piecewise Continuous Dynamical Systems

Abstract

The, “Complex systems”, stands as a broad term for many diverse disciplines of science and engineering including natural & medical sciences. Complexities appearing in various dynamical systems during evolution are now interesting subjects of studies. Chaos appearing in various dynamical systems can also be viewed as a form of complexity. For some cases nonlinearities within the systems and for other cases piecewise continuity property of the system are responsible for such complexity. Dynamical systems represented by mathematical models having piecewise continuous properties show strange complexity character during evolution. Interesting recent articles explain widely on complexities in various systems. Observable quantities for complexity are measurement of Lyapunov exponents (LCEs), topological entropies, correlation dimension etc. The present article is related to study of complexity in systems having piecewise continuous properties. Some mathematical models are considered here in this regard including famous Lozi map, a discrete mathematical model and Chua circuit, a continuous model. Investigations have been carried forward to obtain various attractors of these maps appearing during evolution in diverse and interesting pattern for different set of values of parameters and for different initial conditions. Numerical investigations extended to obtain bifurcation diagrams, calculations of LCEs, topological entropies and correlation dimension together with their graphical representation.