Harmless delays and global attractivity for nonautonomous predator-prey system with dispersion

AbstractIn this paper, we consider a nonautonomous predator-prey model with dispersion and a finite number of discrete delays. The system consists of two Lotka-Volterra patches and has two species: one can disperse between two patches, but the other is confined to one patch and cannot disperse. Our purpose is to demonstrate that the time delays are harmless for uniform persistence of the solutions of the system. Furthermore, we establish conditions under which the system admits a positive periodic solution which attracts all solutions

The effect of diffusion on the time varying logistic population growth

AbstractIn this paper, we consider the effect of diffusion on the species that live in changing patches environment. Different from the former studies [1–4], we pay attention to the more important situation in conservation biology that species live in a weak patches environment, in the sense that species in some of the isolated patches will be extinct without the contribution from other patches. We obtain an interesting result: the identical species can persist for some diffusion rates, and can also vanish for another set of restriction on diffusion rates

Permanence and positive periodic solution for the single-species nonautonomous delay diffusive models

AbstractSingle-species nonautonomous delay diffusion models with nonlinear growth rates are investigated. Some sufficient conditions are determined that guarantee the permanence of the species and the existence of a positive periodic solution which is global attractively

Permanence and periodicity of a delayed ratio-dependent predator–prey model with Holling type functional response and stage structure

AbstractA periodic and delayed ratio-dependent predator–prey system with Holling type III functional response and stage structure for both prey and predator is investigated. It is assumed that immature predator and mature individuals of each species are divided by a fixed age, and immature predator do not have the ability to attack prey. Sufficient conditions are derived for the permanence and existence of positive periodic solution of the model. Numerical simulations are presented to illustrate the feasibility of our main results

Global Dynamics Behaviors of Viral Infection Model for Pest Management

According to biological strategy for pest control, a mathematical model with periodic releasing virus particles for insect viruses attacking pests is considered. By using Floquet's theorem, small-amplitude perturbation skills and comparison theorem, we prove that all solutions of the system are uniformly ultimately bounded and there exists a globally asymptotically stable pest-eradication periodic solution when the amount of virus particles released is larger than some critical value. When the amount of virus particles released is less than some critical value, the system is shown to be permanent, which implies that the trivial pest-eradication solution loses its stability. Further, the mathematical results are also confirmed by means of numerical simulation

Dynamic Analysis of a Predator-Prey (Pest) Model with Disease in Prey and Involving an Impulsive Control Strategy

The dynamic behaviors of a predator-prey (pest) model with disease in prey and involving an impulsive control strategy to release infected prey at fixed times are investigated for the purpose of integrated pest management. Mathematical theoretical works have been pursuing the investigation of the local asymptotical stability and global attractivity for the semitrivial periodic solution and population persistent, which depicts the threshold expression of some critical parameters for carrying out integrated pest management. Numerical analysis indicates that the impulsive control strategy has a strong effect on the dynamical complexity and population persistent using bifurcation diagrams and power spectra diagrams. These results show that if the release amount of infective prey can satisfy some critical conditions, then all biological populations will coexist. All these results are expected to be of use in the study of the dynamic complexity of ecosystems

Dynamic Complexity of an Ivlev-Type Prey-Predator System with Impulsive State Feedback Control

The dynamic complexities of an Ivlev-type prey-predator system with impulsive state feedback control are studied analytically and numerically. Using the analogue of the Poincaré criterion, sufficient conditions for the existence and the stability of semitrivial periodic solutions can be obtained. Furthermore, the bifurcation diagrams and phase diagrams are investigated by means of numerical simulations, which illustrate the feasibility of the main results presented here

One-step synthesis of thermally stable artificial multienzyme cascade system for efficient enzymatic electrochemical detection

Abstract(#br)Recently, metal-organic framework (MOF)-based multienzyme systems integrating different functional natural enzymes and/or nanomaterial-based artificial enzymes are attracting increasing attention due to their high catalytic efficiency and promising application in sensing. Simple and controllable integration of enzymes or nanozymes within MOFs is crucial for achieving efficient cascade catalysis and high stability. Here, we report a facile electrochemical assisted biomimetic mineralization strategy to prepare an artificial multienzyme system for efficient electrochemical detection of biomolecules. By using the GO x @Cu-MOF/copper foam (GO x @Cu-MOF/CF) architecture as a proof of concept, efficient enzyme immobilization and cascade catalysis were achieved by in situ..