On the asymptotic stability of a rational multi-parameter first order difference equation
Abstract
In this part we study the dynamics of the following rational multi-parameter first order difference equation xn+1 =(axn3+ bxn2+cxn + d)/xn3, x0∈ R+ where the parameters a, b, d together with the initial condition x0 are positive while the parameter c could accept some negative values. We investigate the equilibria and 2-cycles of this equation and analyze qualitative and asymptotic behavior of it's solutions such as convergence to an equilibrium or to a 2-cycle.
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