Controlling the diffusionless Lorenz equations with periodic parametric perturbation

Abstract

a b s t r a c tDiffusionless Lorenz equations (DLE) are a simple one-parameter version of the wellknown Lorenz model, which was obtained in the limit of high Rayleigh and Prandtl numbers, physically corresponding to diffusionless convection. A simple control method is presented to control chaos by using periodic parameter perturbation in DLE. By using the generalized Melnikov method, the parameter conditions could be obtained to guide the controlled DLE to a low-periodic motion. Moreover, the existence conditions of periodic orbits and homoclinic orbits in the system are given. Some results of the numerical simulation are also explained clearly by a rigorous analysis.

A piecewise spectral method for solving the chaotic control problems of hyperchaotic finance system

“…In the recent years, a great effort has been devoted towards the chaos control, including stabilization of unstable equilibrium points, and more generally, unstable periodic solutions . Particularly, in case of chaos suppression of known chaotic systems, some useful methods have been developed.…”

“…In the recent years, a great effort has been devoted towards the chaos control, including stabilization of unstable equilibrium points, and more generally, unstable periodic solutions. 7 Particularly, in case of chaos suppression of known chaotic systems, some useful methods have been developed. These include adaptive control, adaptive fuzzy control, sliding mode control, Robust control, time-delayed feedback control, bang-bang control, optimal control, intelligent control, etc.…”

Periodic parametric perturbation control for a 3D autonomous chaotic system and its dynamics at infinity

“…In Ref. [28,30], periodic parametric perturbation control method was presented in Lorenz equations and diffusionless Lorenz equations. From the above point of view, we can see that the study of constructing simple chaotic systems and analysis of periodic orbits construct for the systems are of highly practical importance.…”

Synchronization between Fractional-Order and Integer-Order Hyperchaotic Systems via Sliding Mode Controller

“…During the past decades, fractional calculus has become a powerful tool to describe the dynamics of complex systems such as power systems, mathematics, biology, medicine, secure communication, and chemical reactors [1][2][3][4][5][6]. Chaos synchronization has attracted lots of attention in a variety of research fields [7][8][9][10][11][12][13] over the last two decades, because it can be applied in vast areas of physics and engineering and secure communication [14,15].…”