Asymptotic properties of solutions of the difference equation of the form are studied. Conditions under which every (every bounded) solution of the equation is asymptotically equivalent to some solution of the above equation are obtained.
Asymptotic properties of solutions of difference equation of the form are studied. Conditions under which every (every bounded) solution of the equation is asymptotically equivalent to some solution of the above equation are obtained. Moreover, the conditions under which every polynomial sequence of degree less than is asymptotically equivalent to some solution of the equation and every solution is asymptotically polynomial are obtained. The consequences of the existence of asymptotically...
Using the method of variation of constants, discrete inequalities and Tychonoff’s fixed-point theorem we study problem asymptotic equivalence of second order difference equations.
We study the asymptotics of first-order nonlinear difference equations. In particular we present an asymptotic functional equation for potential asymptotic behaviour, and a theorem stating sufficient conditions for the existence of an actual solution with such asymptotic behaviour.
The dynamics of a discrete-time predator-prey model with Holling-IV functional response are investigated. It is shown that the model undergoes a flip bifurcation, a Hopf bifurcation and a saddle-node bifurcation by using the center manifold theorem and bifurcation theory. Numerical simulations not only exhibit our results with the theoretical analysis, but also show the complex dynamical behaviors, such as the period-3, 6, 9, 12, 20, 63, 70, 112 orbits, a cascade of period-doubling bifurcations...