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This paper studies the effect of time delay and proportional harvesting on stability of mutualism model as well as to establish conditions for sustainable harvesting so that the unique positive equilibrium point is stable. First the stability of the model with harvesting is analyzed. The model is then improved by considering a time delay in the mechanism of the growth rate of the population. The analysis...
A three-stage-structured prey-predator system with predator density dependent time delay is considered. The positive and uniformly bounded of the solution of the system are obtained, and the conditions for the system occurring global Hopf bifurcation is given. Finally, numerical simulations and brief conclusion are given.
In this paper, a delayed worm propagation model with birth and death rates is discussed. The number of system reinstallations may be increased when the hosts get unstable (infected or quarantined). In view of such situation, dynamic birth and death rates are introduced. Afterwards, the stability of the positive equilibrium is studied. Through the theoretical analysis, it is proved that the model is...
In this paper, a predator-prey system is proposed which changes the roles of predator and prey when the prey becomes adult. Through investigating, sufficient conditions have been obtained for boundedness of solutions and permanence of the proposed model. By using bifurcation theory, Hopf bifurcation occurs as the time delay increases through a critical value. At last, numerical simulations are carried...
This paper deals with the problem of exponential stability for a class of discrete-time recurrent neural networks with time-varying delay by employing an improved free-weighting matrix approach. The relationship among the time-varying delay, its upper bound and their difference is taken into account. As a result, a new and less conservative delay-dependent stability criterion is obtained without ignoring...
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