On a conjecture for a higher-order rational difference equation.
Dynamical behavior for a stochastic two-species competitive model
This paper deals with a stochastic two-species competitive model. Some very verifiable criteria on the global stability of the positive equilibrium of the deterministic system are established. An example with its computer simulations is given to illustrate our main theoretical findings.
Dynamics in a discrete predator-prey system with infected prey
In this paper, a discrete version of continuous non-autonomous predator-prey model with infected prey is investigated. By using Gaines and Mawhin's continuation theorem of coincidence degree theory and the method of Lyapunov function, some sufficient conditions for the existence and global asymptotical stability of positive periodic solution of difference equations in consideration are established. An example shows the feasibility of the main results.
Stability and Hopf bifurcation analysis for a Lotka-Volterra predator-prey model with two delays
In this paper, a two-species Lotka-Volterra predator-prey model with two delays is considered. By analyzing the associated characteristic transcendental equation, the linear stability of the positive equilibrium is investigated and Hopf bifurcation is demonstrated. Some explicit formulae for determining the stability and direction of Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using normal form theory and center manifold theory. Some numerical simulations...
Existence and global attractivity of positive periodic solutions for a delayed competitive system with the effect of toxic substances and impulses
In this paper, a class of non-autonomous delayed competitive systems with the effect of toxic substances and impulses is considered. By using the continuation theorem of coincidence degree theory, we derive a set of easily verifiable sufficient conditions that guarantees the existence of at least one positive periodic solution, and by constructing a suitable Lyapunov functional, the uniqueness and global attractivity of the positive periodic solution are established.
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