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Chaotification of discrete dynamical systems
(Maltepe Üniversitesi, 2009) Ikhlef, A.; Mansouri, N.
Chaos has been extensively studied within the scientific, engineering and mathematical communities as an interesting complex dynamic phenomenon. Recently, the traditional trend of understanding and analyzing chaos has evolved to a new phase of investigation: controlling and creating chaos. More specifically, when chaos is useful, it is generate intentionally. However, when chaos is harmful, it is controlled. Indeed, several studies have showed that chaos can be useful or has great potential in many disciplines such as in high-performance circuit design for telecommunication, collapse prevention of power systems or biomedical engineering applications to the human brain and heart. Therefore, creating chaos becomes a key issue in such applications where chaos is important and useful [1, 2]. In a sequence of papers, the problem of chaotification of discrete systems is addressed [3, 4, 5, 6]. In a recent paper a closed expression was provided for the controller, in terms of the system state vector and a set of specified Lyapunov exponents. According to the stability theorems, a dynamical system is stable if and only if all its Lyapunov exponents are lower or equal to zero. If at least one is positive, the system becomes completely unstable. For this, practically all methods of chaotification are based on the change of sign of the Lyapunov exponent .