Bifurcation and control of chaos in a chemical system

This paper is devoted to investigate the problem of controlling chaos in a chaotic chemical system. The feedback method is used to suppress chaos to unstable equilibria or unstable periodic orbits. The Routh–Hurwitz criteria is applied to analyze the conditions of the asymptotic stability of the positive equilibrium. By choosing the delay as bifurcation parameter, we investigate what effect the delay has on the dynamics of the chemical system with delayed feedback. It is shown that the positive equilibrium is locally asymptotically stable when the time delay is sufficiently small, as the time delay passes through a sequence of critical values, then the positive equilibrium will lose its stability and a bifurcating periodic solution will occur. By using the normal form theory and center manifold argument, we derive the explicit formulae for determining the stability, the direction and the period of bifurcating periodic solutions. Finally, numerical simulation is provided to show the effectiveness of the proposed control method.