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Abstract: We consider a family of singular maps as an example of a simple model ofdynamical systems exhibiting the property of robust chaos on a well definedrange of parameters. Critical boundaries separating the region of robust chaosfrom the region where stable fixed points exist are calculated on the parameterspace of the system. It is shown that the transitions to robust chaos in thesesystems occur either through the routes of type-I or type-III intermittency andthe critical boundaries for each type of transition have been determined on thephase diagram of the system. The simplicity of these singular maps and therobustness of their chaotic dynamics make them useful ingredients in theconstruction of models and in applications that require reliable operationunder chaos.



Author: M. G. Cosenza, O. Alvarez-LLamoza

Source: https://arxiv.org/



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