DUFFING-VAN DER POL'S EQUATION

B ifurcation of periodic oscillations and chaotic states in a system described by the Duffing- van der Pol's equation are considered. By using digital computers, bifurcation sets of periodic solutions are calculated. S tructure of invariant curves in the harmonic entrained region are studied. The strange attractor and the strange repellor obtained in the system are given. Correlations between chaotic oscillations and unstable periodic p oints This paper deals with the bifurcation of periodic oscillations, and with the occurrence of chaotic states in a system described by the Duffing-van der Pol's equation. The equation has nonlinear restoring terms. It has been reported that, when the restoring terms contain a negative linear term, the solutions are very complicated(11. In the following, we consider the oscillations occurring in a system of this kind. The behaviors of the system can be studied by using the Poincar; map for the solution of the equation. Making use of digital computers, the entrained regions of harmonic oscillations a re obtained by calculating the bifurcation sets of the periodic solutions. We consider the structure of invariant curves in the entrained regions. Then we investigate correlations between unstable periodic p oints and chaotic oscilla- tions.