Hyperchaos–chaos–hyperchaos transition in modified Rössler systems

We consider in this paper a family of modified hyperchaotic Rössler systems and investigate both problems of understanding hyperchaos–chaos–hyperchaos transition and computing the prediction time. These systems were obtained and numerically investigated by Nikolov and Clodong [Nikolov S, Clodong S. Occurrence of regular, chaotic and hyperchaotic behavior in a family of modified Rossler hyperchaotic systems. Chaos, Solitons & Fractals 2004;22:407–31]. Our studies confirm that transition hyperchaos–chaos–hyperchaos (i) depends on the change of the sign of the corresponding characteristic equation roots or (ii) can be obtained as a result of the absorption/repulsion of the repeller originally located out of the attractor by the growing attractor. It is also shown that the prediction time is a more reliable predictor of the evolution than the information dimension. We conclude that the prediction time in hyperchaotic regimes is at least one order of magnitude smaller than those in chaotic zones.