LIMIT CYCLE & BUTTERFLY ATTRACTOR FROM LOGISTIC DIFFERENTIAL EQUATIONS WITH VANDER POL CIRCUIT

Van der pol is a classic example of self-oscillatory system of logistic differential equation. It is second order ordinary differential equation with two dimension phase space. It can be applied to physics, electronics, biology, neurology, sociology and economics so we can say that the model also approaches to chaotic behavior due to its nature of nonlinearity. It was first chaotic oscillator Van der Pol circuit is originally an electronic circuit. We have taken this classical problem in our work because this was the first electronic circuit, which shows results related with our work chaotic behavior of the system of logistic equations, like bifurcation, limit cycles and relaxation oscillations. It is useful to explore the concept of nonlinear dynamics and serves as a starting point for nonlinear and chaotic systems of logistic equations. Here we have also taken the MATLAB output of the oscillator which gave us the attractive results of the Limit cycle which is similar to those attractors that came as the output of the Lorenz attractor in the form of Butterfly (Lorenz 1963).