Dynamics of weakly dissipative self-oscillatory system at external pulse influence, which amplitude is depending polynomially

Topic and aim. In this work, we study the dynamics of the kicked van der Pol oscillator with the amplitude of kicks depending nonlinearly on the dynamic variable. We choose the expansions of the function $\cos x$ in a Taylor series near zero, as functions describing this dependence. It is known that such a system demonstrates the existence of a Hamiltonian-type critical point in the case when the dependence of the amplitude of an external force on a dynamic variable is described by a quadratic polynomial, and when choosing a dependence in the form of $\cos x$ – a stochastic web in the conservative limit. Investigated models. The investigation is conducted for the original flow system and for an approximate discrete mapping. Results. We have investigated the changes in the structure of the parameter space and the phase space when changing the form of the function of external force. It is shown that the complication of the form of the function leads to an increase in the number of saddle-node bifurcations occurring in the system with a decrease in the dissipation parameter.