Narrow Results

In this paper, a population system with cross-diffusion and habitat complexity is selected as study object. We investigate that how cross-diffusion and habitat complexity destabilize the otherwise stable periodic solutions of the ODEs to generate the new abundant spatial Turing patterns. By utilizing the local Hopf bifurcation theorem and perturbation theory, we establish a formula to determine the Turing instability of periodic solutions of the population system with cross-diffusion and habitat complexity. Finally, numerical simulations are performed to verify theoretical analysis, simultaneously, we verify the formation process of spatial Turing patterns when the cross-diffusion coefficients and habitat complexity change.

A delay-induced nonautonomous predator–prey system with variable habitat complexity is proposed based on mathematical and ecological issues, and this system is more realistic than the published models. Firstly, the permanence of the nonautonomous predation system is studied and some sufficient conditions are obtained. Secondly, the dynamical behaviors of the corresponding autonomous predation system are investigated, including the positivity and boundedness, and local and global stabilities. Thirdly, the properties of Hopf bifurcation of the autonomous predation system without/with delay are investigated and the explicit formulas which determine the stability and the direction of periodic solutions are obtained. Finally, a numerical example is given to test our theoretical results.

This paper presents a generalized delayed predator–prey system with habitat complexity. First, the dynamical behaviors of the considered system, including positivity and boundedness, stability property and the existence of Hopf bifurcation and super-critical bifurcation without time delay, are analyzed. Second, the effect of time delay on the dynamical behavior of the presented system is considered in four cases, and sufficient conditions for the existence of Hopf bifurcation are obtained. Moreover, the explicit formulas to determine the direction, stability and period of bifurcating periodic solutions are derived by applying the center manifold theory and normal form theory. Finally, numerical simulations are conducted to verify the corresponding theoretical results.

This paper presents a generalized predator–prey system and considers the effect of habitat complexity on the dynamical consequences. The results show that habitat complexity has a major impact on the dynamical consequences of the considered system. On the one hand, habitat complexity has a stabilizing impact under certain conditions. A numerical simulation in our study and in experiments conducted in the published studies elaborate on this stabilizing effect. On the other hand, the most interesting and open issue is that a destabilizing effect of habitat complexity is found theoretically. All results are explained and illustrated from the ecological viewpoint.

This paper investigates a stochastic Holling II predator-prey model with Lévy jumps and habit complexity. It is first proved that the established model admits a unique global positive solution by employing the Lyapunov technique, and the stochastic ultimate boundedness of this positive solution is also obtained. Sufficient conditions are established for the extinction and persistence of this solution. Moreover, some numerical simulations are carried out to support the obtained results.

Considering the food diversity of natural enemy species and the habitat complexity of prey populations, a pest-natural enemy model with non-monotonic functional response is proposed for biological management of Bemisia tabaci. The dynamic characteristics of the proposed model are analyzed. In addition, considering that the conversion from prey to predator has a certain time lag rather than instantaneous, a time delay is introduced into this model, and it is shown that the Hopf bifurcation occurs at the interior equilibrium when the time delay is used as the bifurcation parameter. Furthermore, the values of the parameters that determine the direction of the Hopf bifurcation as well as the stability of the periodic solution are calculated. In order to illustrate the theoretical analysis results, numerical simulations and validation are carried out to demonstrate the effects of non-monotonic functional response, additional food supply and habitat complexity.