Does mutual interference stabilize prey-predator model with Bazykin-Crowley-Martin trophic function?

We investigated a system of ordinary differential equations that describes the dynamics of prey and predator populations, taking into account the Allee effect affecting the reproduction of the predator population, and mutual interference amongst predators, which is modeled with the Bazykin-Crowley-Martin (BCM) trophic function. Bifurcation analysis revealed a rich spectrum of bifurcations occurring in the system. In particular, analytical conditions for the saddle-node, Hopf, cusp, and Bogdanov-Takens bifurcations were derived for the model parameters, quantifying the strength of the predator interference, the Allee effect, and the predation efficiency.

Landscape refuges delay resistance of the European corn borer to Bt-maize: a demo-genetic dynamic model.

We constructed a reaction-diffusion model of the development of resistance to transgenic insecticidal Bt crops in pest populations. Kostitzin's demo-genetic model describes local interactions between three competing pest genotypes with alleles conferring resistance or susceptibility to transgenic plants, the spatial spread of insects being modelled by diffusion. This new approach makes it possible to combine a spatial demographic model of population dynamics with classical genetic theory.

Does mutual interference always stabilize predator-prey dynamics? A comparison of models.

Based on a qualitative analysis of ODE systems, the dynamic properties of alternative predator-prey models with predator-dependent functional response have been compared in order to study the role that predator interference plays in the stabilisation of trophic systems. The models considered for interference have different mathematical expressions and different conceptual foundations. Despite these differences, they give essentially the same qualitative results: when interference is low, increasing it has a positive effect on asymptotic stability and thus on the resilience of the biological system.

Clustering due to Acceleration in the Response to Population Gradient: A Simple Self-Organization Model.

We explore the phenomenon of animal self-organization due to autotaxis, that is, the movement of individuals induced by their own density gradient. There is natural evidence that clustering occurs as a result of the interplay between random and directed movements of individuals due to mutual attraction and repulsion. Classically, it is assumed that taxis velocity is determined by the density gradient of some stimulus.

The role of prey taxis in biological control: a spatial theoretical model.

We study a reaction-diffusion-advection model for the dynamics of populations under biological control. A control agent is assumed to be a predator species that has the ability to perceive the heterogeneity of pest distribution. The advection term represents the predator density movement according to a basic prey taxis assumption: acceleration of predators is proportional to the prey density gradient.