Осциллятор ван дер Поля

Topic. The phenomenological model of ensemble of three neurons coupled by chemical (synaptic) and electrical couplings is studied. Single neuron is modeled by van der Pol oscillator.

We present a way to realize hyperchaotic behavior for a system based on Q­switched van der Pol oscillator with non­linear signal transformation in the delayed feedback loop. The results of numerical studies are discussed: time dependences of variables, attractor portraits, Lyapunov exponents, and power spectrum.

The particular properties of dynamics are discussed for dissipatively coupled van der Pol oscillators, non­identical in values of parameters controlling the Andronov–Hopf bifurcation and nonlinear dissipation. Possibility of a special synchronization regime in an infinitively long band between oscillator death and quasiperiodic areas is shown for such system. Non­identity of parameters of nonlinear dissipation results in specific form of the boundary of the main synchronization tongue, which looks like the mirror letter S.

We present chaos generator based on a van der Pol oscillator with two additional delayed feedback loops. Oscillator alternately enters active and silence stages due to periodic variation of the parameter responsible for the Andronov–Hopf bifurcation. Excitation of the oscillations on each new activity stage is forced by signal resulting from mixing of the first and the second harmonics of signals from previous activity stages, transported through the feedback loops.