In this paper, a rational difference equation with positive parameters and non-negative conditions is used to determine the presence and direction of the Neimark–Sacker bifurcation. The neimark–Sacker bifurcation of the system is first studied using the characteristic equation. In addition, we study bifurcation invariant curves from the perspective of normal form theory. A computer simulation is used to illustrate the analytical results.
We examine the unboundedness, persistence, boundedness, uniqueness, and existence of non-negative equilibrium of an exponential symmetric difference equations system: Ωn+1=α1+β1Ωn+γ1Ωn−1e−(Ωn+ϖn), ϖn+1=α2+β2ϖn+γ2ϖn−1e−(Ωn+ϖn),n=0,1,⋯, whereby initial values Ω−1,ϖ−1,Ω0,ϖ0 and parameters α1,α2 are non-negative real numbers and β1,β2∈(0,1) and γ1,γ2≤0. We will discuss asymptotic global and local stability and the convergence rate of this system. Ultimately, to check our results, we set out some numerical explanations.
The boundedness nature and persistence, global and local behavior, and rate of convergence of positive solutions of a second-order system of exponential difference equations, is investigated in this work. Where the parameters A,B,C,α,β,γ,δ,η, and ξare constants that are positive, and the initials U−1,U0,V−1,V0,W−1, and W0 are non-negative real numbers. Some examples are provided to support our theoretical results.
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