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2020•arXiv (Cornell University)Open access

A new version of distributional chaos and the relations between distributional chaos in a sequence and other concepts of chaos

Hongbo Zeng

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Abstract

In this paper we consider relations between distributional chaos in a sequence with distributional chaos, w-chaos, R-T chaos, DC 3, respectively). We give a sufficient condition and prove that the distributional chaos is equivalent to the distributional chaos in a sequence under this condition. Besides, we get that distributional chaos in a sequence and w-chaos(R-T chaos, DC 3, respectively)do not imply each other. Finally, we give a new definition of chaos, named DC 2', which is similar to DC 2, and show that for any integer N > 0, f is DC 2' if and only if f^N is also DC 2'.

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In this paper we consider relations between distributional chaos in a sequence with distributional chaos, w-chaos, R-T chaos, DC 3, respectively). We give a sufficient condition and prove that the distributional chaos is equivalent to the distributional chaos in a sequence under this condition. Besides, we get that distributional chaos in a sequence and w-chaos(R-T chaos, DC 3, respectively)do not imply each other. Finally, we give a new definition of chaos, named DC 2', which is similar to DC 2, and show that for any integer N > 0, f is DC 2' if and only if f^N is also DC 2'.

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Available abstract

In this paper we consider relations between distributional chaos in a sequence with distributional chaos, w-chaos, R-T chaos, DC 3, respectively). We give a sufficient condition and prove that the distributional chaos is equivalent to the distributional chaos in a sequence under this condition. Besides, we get that distributional chaos in a sequence and w-chaos(R-T chaos, DC 3, respectively)do not imply each other. Finally, we give a new definition of chaos, named DC 2', which is similar to DC 2, and show that for any integer N > 0, f is DC 2' if and only if f^N is also DC 2'.

Key concepts: CHAOS (operating system), Sequence (biology), Statistical physics, Chaos theory, Polynomial chaos, Synchronization of chaos, Control of chaos, Computer science

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