A chaotic system with only one stable equilibrium

Horseshoes in a Chaotic System with only One Stable equilibrium

Simple Chaotic flows with One Stable equilibrium

It is widely recognized that mathematically simple systems of nonlinear differential equations can exhibit chaos. With the advent of fast computers, it is now possible to explore the entire parameter space of these systems with the goal of finding parameters that result in some desired characteristics of the system. Recently there has been increasing attention to some unusual examples of such s...

Chaotic behavior and modified function projective synchronization of a simple system with one stable equilibrium

By introducing a feedback control to a proposed Sprott E system, an extremely complex chaotic attractor with only one stable equilibrium is derived. The system evolves into periodic and chaotic behaviors by detailed numerical as well as theoretical analysis. Analysis results show that chaos also can be generated via a period-doubling bifurcation when the system has one and only one stable equil...

Degenerate Hopf bifurcations , hidden attractors , and control in the extended Sprott E system with only one stable equilibrium

In this paper, we introduce an extended Sprott E system by a general quadratic control scheme with 3 arbitrary parameters for the new system. The resulting system can exhibit codimension-one Hopf bifurcations as parameters vary. The control strategy used can be applied to create degenerate Hopf bifurcations at desired locations with preferred stability. A complex chaotic attractor with only one...

Constructing a Novel No-Equilibrium Chaotic System

This paper introduces a new no–equilibrium chaotic system that is constructed by adding a tiny perturbation to a simple chaotic flow having a line equilibrium. Dynamics of the proposed system are investigated through Lyapunov exponents, bifurcation diagram, Poincaré map and period–doubling route to chaos. A circuit realization is also represented. Moreover, two other new chaotic systems without...