Complex dynamics of the system of nonlinear difference equations in the Hilbert space

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.

Keywords

• lotka–volterra models
• population dynamics
• moore–penrose pseudo-inverse operators
• fibonacci numbers