Classification of Chaotic Regimes in the T System by Use of Competitive Modes

We study chaotic behavior of the T system, a three-dimensional autonomous nonlinear system introduced by G. Tigan [Analysis of a dynamical system derived from the Lorenz system, Sci. Bull. Politehnica Univ Timisoara50 (2005) 61–72] which has potential application in secure communications. The recently-developed technique of competitive modes analysis is applied to determine parameter regimes for which the system may exhibit chaotic behavior. We verify that the T system exhibits interesting behaviors in the many parameter regimes thus obtained, thereby demonstrating the great utility of the competitive modes approach in delineating chaotic regimes in multiparemeter systems, where their identification can otherwise involve tedious numerical searches. An additional, novel finding is that one may use competitive modes "at infinity" in order to identify parameter regimes admitting stable equilibria in dynamical models such as the T system.

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