Abstract
AbstractIn the research on chaotic systems, which are used for cryptography and secure communication schemes, a key characteristic is the introduction of novel chaotic systems, usually by adding complexity to the existing ones in order to ensure security. In this direction, this chapter proposes novel chaotic systems, which are the composition of fuzzy numbers with the existing chaotic maps. In particular, the composition of the Gaussian fuzzy number with the logistic, sine, and Chebyshev chaotic maps is introduced. The resulting maps exhibit more complex behaviours compared to their classic counterparts, presenting interesting chaos-related phenomena, such as antimonotonicity, crisis, coexisting attractors, and period doubling route to chaos. To showcase the aforementioned results, the well-known tools for studying the behaviour of chaotic systems are being used, namely bifurcation diagrams and Lyapunov exponent diagrams.KeywordsChaotic systemsFuzzy functionsChaos1-D chaotic mapAntimonotonicityCrisisCoexisting attractors
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