Contrast on two kinds of chaos control on single-species models with harvesting coefficient

Abstract

In allusion to a difference equation of single-species models with harvesting coefficient, the presence of chaotic phenomenon is validated by computing Lyapunov exponent and giving its change with the parameter. Tiny control based on the basic ideas in the classical OGY method and tracking control based on the exact feedback linearization are used to control chaos in the model respectively, we obtain the following results: 1)the sufficient conditions of the species that stabilizes in the fixed points and the trajectory of period-2 are obtained and chaotic phenomenon is eliminated; 2)any orbits can be reached by using tracking control method. Contrast on two kinds of control method, we draw the conclusion that tracking control method is more flexible than the OGY method. The effectiveness of the conclusions are validated by simulation.