On new chaotic and hyperchaotic systems: A literature survey

This paper provides a thorough survey of new chaotic and hyperchaotic systems. An analysis of the dynamic behavior of these complex systems is presented by pointing out their originality and elementary characteristics. Recently, such systems have been increasingly used in various fields such as secure communication, encryption and finance and so on. In practice, each field requires specific performances with peculiar complexity. A particular classification is then proposed in this paper based on the Lyapunov exponent, the equilibriums points and the attractor forms

Periodic orbits bifurcating from a nonisolated zero-Hopf equilibrium of three-dimensional differential systems revisited

In this paper, we study the periodic solutions bifurcating from a nonisolated zero-Hopf equilib- rium in a polynomial differential system of degree two in R³. More specifically, we use recent results of averaging theory to improve the conditions for the existence of one or two periodic solutions bifurcating from such a zero-Hopf equilibrium. This new result is applied for studying the periodic solutions of differential systems in R³ having n-scroll chaotic attractors

Periodic orbits bifurcating from a nonisolated zero-Hopf equilibrium of three-dimensional differential systems revisited

In this paper, we study the periodic solutions bifurcating from a nonisolated zero-Hopf equilib- rium in a polynomial differential system of degree two in R³. More specifically, we use recent results of averaging theory to improve the conditions for the existence of one or two periodic solutions bifurcating from such a zero-Hopf equilibrium. This new result is applied for studying the periodic solutions of differential systems in R³ having n-scroll chaotic attractors