Chaotic and Hyperchaotic Complex Jerk Equations

Chaotic and Hyperchaotic Complex Jerk Equations

The aim of this paper is to introduce and investigate chaotic and hyperchaotic complex jerk equations. The jerk equations describe various phenomena in engineering and physics, for example, electrical circuits, laser physics, mechanical oscillators, damped harmonic oscillators, and biological systems. Properties of these systems are studied and their Lyapunov exponents are calculated. The dynam...

Hypogenetic chaotic jerk flows

Some simple chaotic jerk functions

One of the most remarkable recent developments in classical physics has been the realization that simple nonlinear deterministic equations can have unpredictable ~chaotic! long-term solutions. Chaos is now thought to be rather common in nature, and the study of nonlinear dynamics has brought new excitement to one of the oldest fields of science. The widespread availability of inexpensive person...

Optimized synchronization of chaotic and hyperchaotic systems.

A method of synchronization is presented which, unlike existing methods, can, for generic dynamical systems, force all conditional Lyapunov exponents to go to -∞ . It also has improved noise immunity compared to existing methods, and unlike most of them it can synchronize hyperchaotic systems with almost any single coupling variable from the drive system. Results are presented for the Rossler h...

Dynamical behavior and synchronization of hyperchaotic complex T-system

In this paper, we introduce a new hyperchaotic complex T-system. This system has complex nonlinear behavior which we study its dynamical properties including invariance, equilibria and their stability, Lyapunov exponents, bifurcation, chaotic behavior and chaotic attractors as well as necessary conditions for this system to generate chaos. We discuss the synchronization with certain and uncerta...