2015 Volume 12 Issue 4 Pages 20141116
Attractor merging can exist in chaotic systems with some kind of symmetry, which makes it possible to form a four-wing attractor from a bistable system. A relatively simple such case is described, which has robust chaos varying from a pair of coexisting symmetric single-wing attractors to a double-wing butterfly attractor, and finally to a four-wing attractor. Basic dynamical characteristics of the system are demonstrated in terms of equilibria, Jacobian matrices, Lyapunov exponents, and Poincaré sections. From a broad exploration of the dynamical regions, we observe robust chaos with embedded Arnold tongues of periodicity in selected parameter regions. The chaotic system with a wing structure has four nonlinear quadratic terms, one of the coefficients of which is a hidden isolated amplitude parameter, by which one can control the amplitude of two of the variables. The corresponding chaotic circuit with an amplitude-control knob is designed and implemented, which generates a four-wing attractor with adjustable amplitude.