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Based on biological meaning, a kind of diffusive intraguild predation (IGP: resource, IG prey and IG predator) model with delay effect is investigated in this paper. The model has Holling-Type I functional response between resource-IG prey and resource-IG predator; Holling-Type II functional response between IG prey and IG predator. We first give sufficient conditions on the stability of possible nonnegative constant steady-state solutions for the proposed model, which give us a complete picture of the global dynamics. Then we investigate Hopf bifurcation near the unique positive constant steady-state solution by taking delay as bifurcation parameter and derive the Hopf bifurcation threshold. It is shown that the delay can induce three types of bistability (node-node bistability, node-cycle bistability and cycle-cycle bistability), periodic oscillations and irregular oscillations triggering spatiotemporal chaos in the diffusive IGP model. Numerical simulations are performed to illustrate our theoretical results and suggest that delay can even trigger the emergence of self-organised spatiotemporal patterns, which evolve from spiral patterns to irregular spatial patterns via spatiotemporal Hopf bifurcation. In addition, the impact of diffusion on the model’s dynamics under certain time delay are also explored. [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: In this paper, a class of second-order impulsive Hamiltonian systems are considered. Some new existence results are obtained by using a variational method and critical point theorem due to Tang and Wu. Some recent results are extended. Three examples are presented to illustrate the feasibility and effectiveness of our results. [Copyright &y& Elsevier]

Abstract: In this paper, a p-Laplacian boundary value problem with impulsive effects is considered. Multiplicity of solutions is obtained by three critical points theorem. An example is presented to illustrate main result. [Copyright &y& Elsevier]

Abstract: This paper investigates the existence of multiple periodic solutions for impulsive Gause-type ratio-dependent predator–prey systems with non-monotonic numerical responses and time delays. Some sufficient conditions are derived by using the continuation theorem of coincidence degree theory and analysis technique. As corollaries, some applications are listed. In particular, the presented criteria improve and extend many previous results in the literature. [Copyright &y& Elsevier]

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, 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: In this paper, by using an abstract continuous theorem of k-set contractive operator, the criteria is established for the existence, global attractivity of positive periodic solution of a neutral delay Logarithmic population model with multiple delays. The result improve the known ones in [S.P. Lu, W.G. Ge, Existence of positive periodic solutions for neutral Logarithmic population model with multiple delays, J. Comput. Appl. Math. 166 (2) (2004) 371–383]. [Copyright &y& Elsevier]

This paper is concerned with a delay differential system with piecewise constant nonlinearity. Such a differential system can be regarded as a model of two-neuron artificial neural network with delayed feedback. Some interesting results are obtained for the convergence and periodicity of solutions of the system. [Copyright &y& Elsevier]