A New Chaotic System with a Pear-shaped Equilibrium and its Circuit Simulation

This paper reports the finding a new chaotic system with a pear-shaped equilibrium curve and makes a valuable addition to existing chaotic systems with infinite equilibrium points in the literature. The new chaotic system has a total of five nonlinearities. Lyapunov exponents of the new chaotic system are studied for verifying chaos properties and phase portraits of the new system are unveiled. An electronic circuit simulation of the new chaotic system with pear-shaped equilibrium curve is shown using Multisim to check the model feasibility

A New Chaotic System with Line of Equilibria: Dynamics, Passive Control and Circuit Design

A new chaotic system with line equilibrium is introduced in this paper. This system consists of five terms with two transcendental nonlinearities and two quadratic nonlinearities. Various tools of dynamical system such as phase portraits, Lyapunov exponents, Kaplan-Yorke dimension, bifurcation diagram and Poincarè map are used. It is interesting that this system has a line of fixed points and can display chaotic attractors. Next, this paper discusses control using passive control method. One example is given to insure the theoretical analysis. Finally, for the  new chaotic system, An electronic circuit for realizing the chaotic system has been implemented. The numerical simulation by using MATLAB 2010 and implementation of circuit simulations by using MultiSIM 10.0 have been performed in this study

A new three-dimensional chaotic system with a cloud-shaped curve of equilibrium points, its circuit implementation and sound encryption

In the chaos literature, significant attention has been paid to chaotic systems with uncountable equilibrium points such as chaotic systems with line equilibrium, curve equilibrium, etc. This paper reports a novel chaotic system with a cloud-shaped curve of equilibrium points with symmetry properties. A new control law for completely synchronising the new chaotic system with cloud-shaped equilibrium curve has been established via adaptive integral sliding mode control. Also, an electronic circuit implementation of the theoretical system is designed to check its feasibility. As an engineering application, new results are derived for sound encryption with the new chaotic system