Morse Decompositions for Delay-Difference Equations

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Abstract

Scalar difference equations x k+1 = f(x k , x k-d ) with delay d∈ N are well-motivated from applications e.g. in the life sciences or discretizations of delay-differential equations. We investigate their global dynamics by providing a (nontrivial) Morse decomposition of the global attractor. Under an appropriate feedback condition on the second variable of f, our basic tool is an integer-valued Lyapunov functional.

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Garab, Á., & Pötzsche, C. (2019). Morse Decompositions for Delay-Difference Equations. Journal of Dynamics and Differential Equations, 31(2), 903–932. https://doi.org/10.1007/s10884-018-9685-8

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