International Journal of Biomathematics

This paper studies a periodic coefficients predator-prey delay system with mixed functional response, in which the prey has a history that takes them through two stages, immature and mature. Also, the total toxic action on the predator population expressed by an integral term is considered in our system. Furthermore, the feedback control is considered in our system. Sufficient conditions which guarantee the permanence and extinction of the system are obtained. Finally, we give a brief discussion of our results. From a biological point of view, our results can be used to help protect beneficial animals.

In this paper, a harvesting fishery model in a two-patch environment: one free-fishing zone and the other one reserved zone where fishing is strictly prohibited, is proposed and analyzed. The existence of possible biological steady states, along with their local stability, instability and global stability is discussed. The existence of bioeconomic equilibrium is derived. An optimal harvesting policy is also given by applying pontryagin's maximum principle.

In this paper, a discrete n-species Lotka–Volterra type food-chain system with time delays and feedback controls is proposed. By applying the comparison theorem of difference equation, sufficient conditions are obtained for the permanence of the system.

In this paper, we consider a predator-prey system with stage structure. The populations have two stages, an immature stage and a mature stage, the age to maturity is represented by a time delay, which leads to systems of retarded functional differential equations. We obtain the conditions for global asymptotic stability of two nonnegative equilibria of this system. The numerical simulation suggests that time delay has both oscillatory dynamics and stabilizing effects.

In this paper, we considered an eco-epidemic model with impulsive birth. By using the coincidence degree theorem, a set of easily verifiable sufficient conditions are obtained for the existence of at least one strictly positive periodic solutions.

A two-species Gause-type ratio-dependent predator-prey system with time delay in a two-patch environment is investigated. By using a continuation theorem based on coincidence degree theory, we establish easily verifiable criteria for the existence of periodic solution for the system. As corollaries, some applications are listed. In particular, our results extend and improve some known results.

By employing a fixed point theorem in cones, this paper investigates the existence of almost periodic solutions for an impulsive logistic equation with infinite delay. A set of sufficient conditions on the existence of almost periodic solutions of the equation is obtained.

In the paper, according to biological and chemical control strategy for pest control, our main purpose is to construct a three trophic level food chain system with Holling IV functional responses and periodic constant impulsive effect concerning integrated pest management (IPM), and investigate the dynamic behaviors of this system. By using the Floquet theory and comparison theorem of impulsive differential equation and analytic method, we prove that there exists a globally asymptotically stable pest-eradication periodic solution when the impulsive period is less than some critical value. Further, condition for permanence of the system is established. Finally, numerical simulation shows that there exists a stable positive periodic solution with a maximum value no larger than a given level.

In this paper, a system of retarded functional differential equations is proposed as a predator-prey model with disease in the prey. The invariance of non-negativity, nature of boundary equilibrium and global stability are analyzed. It also shows that positive equilibrium is locally asymptotically stable when time delay τ = τ₁ + τ₂ is suitable small, while a loss of stability by a Hopf bifurcation can occur around the positive equilibrium as the delays increase.

In this paper, we have proposed a modified neutral delay competitive differential equation model of the growth of two species of plankton having competitive and allelopathic effects on each other. By means of an abstract continuous theorem of k-set contractive operator and some analysis technique. Sufficient conditions are obtained for periodic solution.

Traditional approaches for phylogenetic analysis require a multiple alignment and therefore are not directly applicable to complete genomes, besides, all of these methods assume some sort of an evolutionary model which may not always be correct. We propose a new sequence distance based on the relative information between the sequences using discrimination measure. By making use of the obtained distance matrix, we construct a phylogenic tree for eutherians using the mitochondrial proteins. The examination of topology belong to 20 species illustrates the utility of our approach.