EXISTENCE OF A PERIODIC SOLUTION IN A CHUA'S CIRCUIT WITH SMOOTH NONLINEARITY

摘要

In this paper, we consider Chua's circuit: εu'=z + f(u), z'=u + w - z, w' = -βz - γw, where f(u) is chosen as a cubic function, β > 0 and γ≥ 0 are constants, and ε > 0 is a small parameter. We prove that the flow defines a Poincare map from a compact set which is homeomorphic to the unit disk to itself and then apply Brouwer's fixed-point theorem to conclude that the system has a "big" periodic solution. This global analysis is viewed as a step towards understanding chaos in this model analytically.