MULTISTABILITY IN A BUTTERFLY FLOW

Abstract

A dynamical system with four quadratic nonlinearities is found to display a butterfly strange attractor. In a relatively large region of parameter space the system has coexisting point attractors and limit cycles. At some special parameter combinations, there are five coexisting attractors, where a limit cycle coexists with two equilibrium points and two strange attractors in different attractor basins. The basin boundaries have a symmetric fractal structure. In addition, the system has other multistable regimes where a pair of point attractors coexist with a single limit cycle or a symmetric pair of limit cycles and where a symmetric pair of limit cycles coexist without any stable equilibria.