Qualitative Analysis Of Second Order Nonlinear Difference Equations And Differential Equations

In this paper we study invatiant intervals)the global asymptotic stability and theoscillation of the positive solution of the second order nonlinear difference equation Y_n+1=(?),and discuss invariant intervals,the global asymptotic stability of the positivesolution of the the second order rational difference equation X_n+1=(?),where parameters a,b,A,B,C,α,β,γ>0,and C≥B.In addition,we consider the second order nonlinear differential equation(Gompertzmodel existing reserve area with delay)andand discuss the combined effects of harvesting and time delay on these models.weobtain the global asymptotic stability,the sufficient-necessary condition for the existenceof the positive solution,and the optimal harvesting policy without delay;otherwise,somesufficient conditions which ensure the stability of the positive solution with delay are provided,where parameters r,s,Q,σ1,σ2,K,L,τ>0,and 0≤E≤E_max.