Localization of hidden Chuaʼs attractors

The classical attractors of Lorenz, Rossler, Chua, Chen, and other widely-known attractors are those excited from unstable equilibria. From computational point of view this allows one to use numerical method, in which after transient process a trajectory, started from a point of unstable manifold in the neighborhood of equilibrium, reaches an attractor and identifies it. However there are attractors of another type: hidden attractors, a basin of attraction of which does not contain neighborhoods of equilibria. In the present Letter for localization of hidden attractors of Chuaʼs circuit it is suggested to use a special analytical–numerical algorithm.

► There are hidden attractors: basin doesnʼt contain neighborhoods of equilibria. ► Hidden attractors cannot be reached by trajectory from neighborhoods of equilibria. ► We suggested special procedure for localization of hidden attractors. ► We discovered hidden attractor in Chuaʼs system, L. Chua in his work didnʼt expect this.