Horseshoes chaos and its passive control in dissipative nonlinear chemical dynamics

This work deals with the passive control of horseshoes chaos in dissipative nonlinear chemical oscillations which concentration dynamics are governed by a forced modified Van der Pol-Duffing oscillator. We considered the dynamics of nonlinear chemical systems subjected to fluctuating hydrodynamic drag forces. The influences of the such parameter of the control force on the depth of asymmetric double well potential are analyzed. The Melnikov method is utilized to analytically determine the domains boundaries where horseshoes chaos appears in chemical oscillations. The effects of the constraint parameter β and of the control parameters in the all directions of passive control force are analyzed. Results of analytical investigations are validated and complemented by numerical simulations for draw the fractal basin of attraction and the efficiency of the control force is discussed.