Search

The purpose of this paper is to investigate a diffusive intraguild predation model with intraspecific competition and double free boundaries in one-dimensional space. By adapting existing techniques, we first prove the existence and uniqueness, regularity and uniform estimates of global solution. Then, in terms of parameters range, we show that a spreading-vanishing dichotomy for this free boundary problem. The long time behaviors of (R , N , P) and criteria for spreading and vanishing are also obtained. Additionally, when spreading happens, we propose an upper bound and a lower bound for the asymptotic spreading speeds of the free boundaries. Moreover, numerical simulations are provided to confirm our theoretical results. This paper is an improvement and extension of literatures [Zhang DW, Dai BX. A free boundary problem for the diffusive intraguild predation model with intraspecific competition. J Math Anal Appl. 2019;474:381–412; Zhang DW, Dai BX. Spreading and vanishing in a diffusive intraguild predation model with intraspecific competition and free boundary. Math Methods Appl Sci. 2019;42:6917–6943]. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the spatiotemporal pattern formation in a diffusive intraguild predation (IGP) model with a nonlocal interaction term in the growth of the shared resource, which extends previous studies of local reaction-diffusion IGP model. We first perform the stability and Hopf bifurcation analyses for the unique positive equilibrium of the corresponding non-spatial system, and give analytical formulas to determine the direction and stability of the bifurcating periodic solutions. Then the linear stability analysis for the nonlocal model shows that the nonlocal interaction is a key mechanism for the formation of Turing patterns. Numerical simulations show that low conversion rate from resource to IG predator can induce stationary Turing patterns, intermediate conversion rate can induce regular oscillatory patterns, and high conversion rate can induce irregular spatiotemporal chaotic patterns for certain diffusive rate. The impact of nonlocal interaction on the resulting patterns with certain diffusive rate is further explored by numerical simulations, which show that nonlocal interaction can induce pattern transition from stationary Turing patterns to non-stationary oscillatory patterns, and even to spatiotemporal chaotic patterns with the increase of the nonlocal interaction tensity. In addition, spatiotemporal chaotic patterns are found in the Turing-Hopf parametric space, which enrich pattern dynamics for diffusive IGP models with nonlocal interactions. [ABSTRACT FROM AUTHOR]

A delayed intraguild predation (IGP) model with intraspecific competition is considered. It is shown that the delay has a destabilizing effect and induces oscillations. The global existence results of periodic solutions bifurcating from the positive equilibrium are established. It is shown that there exists at least one nontrival periodic solution when the delay passes through a certain critical value. Numerical simulations are performed to illustrate our theoretical results and show that intraspecific competition can also affect the stability of the positive equilibrium of the system. [ABSTRACT FROM AUTHOR]

We propose a kind of delayed diffusive intraguild predation model with Holling II functional response in this paper. By analyzing the eigenvalue spectrum, it is found that the stability or instability of equilibria can be induced by delay. By utilizing the local bifurcation theory of partial functional differential equations, Hopf bifurcation of the proposed system with time delay as bifurcation parameter is investigated. It reveals that the time delay has a destabilizing effect in the intraguild predation model dynamics and a phenomenon of Hopf bifurcation occurs when the delay increases through a certain threshold. Then we give the explicit formulas to determine the direction, stability of Hopf bifurcation by utilizing the normal form method and center manifold reduction for PFDEs. Numerical simulations are performed to illustrate our theoretical results and show that delay and diffusion can induce the system into chaos and even trigger the emergence of different types of spatial patterns, including spiral wave pattern and chaotic wave pattern, which are induced by Hopf instability. [ABSTRACT FROM AUTHOR]

In this paper, the dynamics for a class of state-dependent impulsive predator–prey models with the logistic growth for the predator and prey species are analyzed. By a direct calculation, the existence of a semi-trivial periodic solution is obtained. Based on the geometrical analysis and biological background, the strict threshold value conditions for the existence of positive periodic solutions are depicted. The stabilities of the semi-trivial periodic solution and positive order-1 periodic solutions are proved due to the analogue of Poincaré criterion. Numerical results are carried out to illustrate the feasibility of our main results. [ABSTRACT FROM AUTHOR]

Abstract: Considering the effects of changing environments, delays, impulses and functional response, a one-prey multi-predators system is established in this paper. Using comparison theorem and some analysis techniques, sufficient conditions ensuring the global attractivity of the prey-extinction positive periodic solution and the permanence of the system are obtained. Finally, examples and numerical simulations are given to show the effectiveness of the main results. [Copyright &y& Elsevier]

Abstract: In this paper, an impulsive delay predator–prey model with stage structure and Beddington-type functional response is established. By using the discrete dynamical system determined by the stroboscopic map, we obtain the existence and global attractivity of the predator-extinction periodic solution. By use of the theory on delay and impulsive differential equation, we study the permanence of the system. Finally, an example is given to show the effectiveness of the main results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we propose an impulsive semi-ratio-dependent predator–prey model with dispersion and time delays. By applying the continuation theorem of coincidence degree theory, we establish a set of sufficient conditions on the existence of at least one positive periodic solution. The result not only improves but also generalizes that for the case without pulses. [Copyright &y& Elsevier]

Abstract: An impulsive periodic predator–prey model with Holling-type IV functional response is considered. Using the continuation theorem of coincidence degree theory, we present an easily verifiable sufficient condition on the existence of multiple periodic solutions. It is important to point out that we establish a better estimation on the difference between the supremum and infimum of a differentiable piecewise continuous periodic function. As illustrated in this paper, with the help of this estimation, many existing results can be improved. [Copyright &y& Elsevier]

Abstract: In this paper, a delayed ratio-dependent predator–prey model with monotonic functional response and impulse is investigated. By using the continuation theorem of coincidence degree theory, an easily verifiable sufficient condition for the existence of at least one positive periodic solution is established. In particular, our results generalize some known criteria. [Copyright &y& Elsevier]

Abstract: Based on the predator–prey (natural enemy–pest) system with generalized Holling type III functional response, an impulsive differential system to model the processes of periodically releasing natural enemies and spraying pesticides at different fixed times for pest control is proposed and investigated. It is shown that if the impulsive period is less than a threshold then the pest-eradication periodic solution is globally asymptotically stable; otherwise the system is permanent. When the system is permanent, further influences of the impulsive perturbations are studied by numerical simulation. Numerical simulation indicates that the system may have complex dynamics. [Copyright &y& Elsevier]

In this paper, we consider the impacts of the chemotaxis and delay on the dynamics of a diffusive predator–prey system with fear effect under the Neumann boundary conditions. Regarding chemotaxis coefficient and delay as bifurcation parameters, the existence of the codimension-two Turing–Hopf bifurcation is studied by analyzing the associated characteristic equation. We deduce that chemotaxis-driven Turing bifurcation and discrete delay-driven Hopf bifurcation can occur simultaneously. Finally, spatially homogeneous periodic oscillation, spatial patterns and spatiotemporal patterns appear near Turing–Hopf bifurcation by numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, we study a delayed predator-prey model with impulse and, in particular, the existence of the predator-free periodic solution. We employ the approach and techniques coming from epidemiology and calculate the basic reproduction number for the predator. Using the basic reproduction number, we consider the global attraction of the predator-free periodic solution and uniform persistence of the predator. Our results improve the results by Li and Liu (Adv. Differ. Equ. 2016:42, 2016), where they left the open problem of finding a threshold value that determines the eradication and uniform persistence of the predator. Furthermore, we give some numerical simulations to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, we propose a host-vector-predator model with stage structure for the vector to explore the impact of biological control agents on host-vector dynamics and disease control. Here the total vector population is divided into two physiological subclasses which are immature and mature subclasses. Holling type II functional response is used to portray the interactions between vectors and predators. Stability analysis of the equilibria demonstrates that the basic reproduction number gives the threshold condition determining the persistence and extinction of the disease. Furthermore, the phenomenon of Hopf bifurcation occurs when predators are introduced. The stability of limit cycle arising from a Hopf bifurcation is rigorously investigated. Finally, numerical simulations are given to show the validity of analytical results, and the comparative results of disease dynamics with and without predators. [ABSTRACT FROM AUTHOR]

In this investigation, we offer and examine a predator–prey interacting model with prey refuge in proportion to both the species and Beddington–DeAngelis functional response. We first prove the well-posedness of the temporal and spatiotemporal models which are restricted in a positive invariant region. Then for the temporal model, we analyse its temporal dynamics including uniform boundedness, permanence, stability of all feasible non-negative equilibria and show that refugia can induce periodic oscillation via Hopf bifurcation around the unique positive equilibrium; for the spatiotemporal model, we not only investigate its permanence, stability of non-negative constant steady states and Turing instability but also study the existence and non-existence of non-constant positive steady states by Leray–Schauder degree theory. The key observation is that the coefficient of refuge cooperates a significant part in modifying the dynamics of the current system and mediates the population permanence, stability of coexisting equilibrium and even the Turing instability parameter space. Finally, general numerical simulation consequences are given to illustrate the validity of the theoretical results. Through numerical simulations, one observes that the model dynamics shows prey refugia and self-diffusion control spatiotemporal pattern growth to spots, stripe–spot mixtures and stripes reproduction. The outcomes assign that the dynamics of the model with prey refuge is not simple, but rich and complex. Additionally, numerical simulations show that the other model parameters have an important effect on species' spatially inhomogeneous distribution, which results in the formation of spots pattern, mixture of spots and stripes pattern, mixture of spots, stripes and rings pattern and anti-spot pattern. This may improve the model dynamics of the prey refuge on the reaction–diffusion predator–prey system. [ABSTRACT FROM AUTHOR]