Controlling the diffusionless Lorenz equations with periodic parametric perturbation. (English) Zbl 1189.34118

Summary: Diffusionless Lorenz equations (DLE) are a simple one-parameter version of the well-known 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.


34H10 Chaos control for problems involving ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
34E15 Singular perturbations for ordinary differential equations
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