Global Period-Doubling Bifurcation of Quadratic Fractional Second Order Difference Equation

Global Dynamics of Certain Homogeneous Second-Order Quadratic Fractional Difference Equation

We investigate the basins of attraction of equilibrium points and minimal period-two solutions of the difference equation of the form x(n+1) = x²(n-1)/(ax²(n) + bx(n)x(n-1) + cx²(n-1)), n = 0,1, 2,…, where the parameters a,  b, and  c are positive numbers and the initial conditions x₋₁ and x₀ are arbitrary nonnegative numbers. The unique feature of this equation is the coexistence of an equilib...

Naimark-Sacker Bifurcation of Second Order Rational Difference Equation with Quadratic Terms

We investigate the global asymptotic stability and Naimark-Sacker bifurcation of the difference equation xn+1 = F bxnxn−1 + cxn−1 + f , n = 0, 1, . . . with non-negative parameters and nonnegative initial conditions x−1, x0 such that bx0x−1 + cx−1 +f > 0. By using fixed point theorem for monotone maps we find the region of parameters where the unique equilibrium is globally asymptotically stable.

Global dynamics of quadratic second order difference equation in the first quadrant

We investigate the global behavior of a quadratic second order difference equation xnþ1 1⁄4 Axn þ Bxnxn 1 þ Cx 2 n 1 þ Dxn þ Exn 1 þ F; n 1⁄4 0;1; . . . with non-negative parameters and initial conditions. We find the global behavior for all ranges of parameters and determine the basins of attraction of all equilibrium points. 2013 Elsevier Inc. All rights reserved.

Global behaviour of a second order nonlinear difference equation

We describe the asymptotic behaviour and the stability properties of the solutions to the nonlinear second order difference equation xn+1 = xn−1 a + bxnxn−1 , n ≥ 0, for all values of the real parameters a, b, and any initial condition (x−1, x0) ∈ R .

Influence of perturbations on period-doubling bifurcation.