Discrete Chaos-I: Theory
Top Cited Papers
- 19 June 2006
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Circuits and Systems I: Regular Papers
- Vol. 53 (6) , 1300-1309
- https://doi.org/10.1109/tcsi.2006.874181
Abstract
We propose a definition of the discrete Lyapunov exponent for an arbitrary permutation of a finite lattice. For discrete-time dynamical systems, it measures the local (between neighboring points) average spreading of the system. We justify our definition by proving that, for large classes of chaotic maps, the corresponding discrete Lyapunov exponent approaches the largest Lyapunov exponent of a chaotic map when Mrarrinfin, where M is the cardinality of the discrete phase space. In analogy with continuous systems, we say the system has discrete chaos if its discrete Lyapunov exponent tends to a positive number, when Mrarrinfin. We present several examples to illustrate the concepts being introducedKeywords
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