Competitive modes for the Baier–Sahle hyperchaotic flow in arbitrary dimensions

The method of competitive modes has been applied in the literature in order to determine if a given dynamical system exhibits chaos, and can be viewed as providing a sort of necessary condition for the occurrence of chaos. In this way, the method has been used as a diagnostic tool in order to determine parameter regimes for which a certain nonlinear system could exhibit chaos. Presently, we apply the method in order to study the N -dimensional Baier–Sahle hyperchaotic flow. This model is a natural choice, since it is a prototypical model of hyperchaos, yet it is simple enough to be analytically tractable. For the N -dimensional model, we show the existence of up to N −1 competitive modes in the presence of hyperchaos. Interestingly, only two of the mode frequencies are time-variable. So, the Baier–Sahle hyperchaotic flow is an example of a fairly simple high-dimensional hyperchaotic model, which lends itself nicely to a competitive modes analysis. Explicit numerical results are provided for the N =4 and N =5 cases in order to better illustrate our results.