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Rigorous computation of the global dynamics of integrodifference equations with smooth nonlinearities. (English) Zbl 1288.37030
The authors present an automated approach to constructing outer approximations for systems in a class of integro-difference operators with smooth nonlinearities. Chebyshev interpolants and Galerkin projections form the basis for the construction, while analysis and interval arithmetic are used to incorporate explicit error bounds. The results represent a significant advance compared to the approach given by S. Day et al. [SIAM J. Appl. Dyn. Syst. 3, No. 2, 117–160 (2004; Zbl 1059.37068)], extending the nonlinearities that may be studied from low-degree polynomials to smooth functions and the studied portion of phase space from a simulated attracting region to the global maximal invariant set.

37L65 Special approximation methods (nonlinear Galerkin, etc.) for infinite-dimensional dissipative dynamical systems
37M25 Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.)
37N25 Dynamical systems in biology
37B30 Index theory for dynamical systems, Morse-Conley indices
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