Complex dynamic of the system of nonlinear difference equations in the Hilbert space
O.O. Pokutnyi
TL;DR
This paper establishes conditions for solutions of nonlinear difference equations in Hilbert spaces, analyzing bifurcations and applying results to systems like Lotka-Volterra.
Contribution
It provides necessary and sufficient conditions for solutions and explores bifurcation phenomena in nonlinear difference systems within Hilbert spaces.
Findings
Conditions for existence of solutions are derived.
Bifurcation and branching conditions are identified.
Examples include Lotka-Volterra systems.
Abstract
In the given article the necessary and sufficient conditions of the existence of solutions of boundary value problem for the nonlinear system in the Hilbert spaces are obtained. Examples of such systems like a Lotka-Volterra are considered. Bifurcation and branching conditions of solutions are obtained.
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Taxonomy
TopicsMathematical and Theoretical Epidemiology and Ecology Models · Differential Equations and Numerical Methods · Nonlinear Differential Equations Analysis