English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The role of predator evasion mediated by chemical signaling is studied in a diffusive prey–predator model when prey-taxis is taken into account (model A) or not (model B) with taxis strength coefficients [Formula: see text] and [Formula: see text], respectively. In the kinetic part of the models, it is assumed that the rate of prey consumption includes functional responses of Holling, Beddington–DeAngelis or Crowley–Martin. Existence of global-in-time classical solutions to model A is proved in space dimension [Formula: see text] while to model B for any [Formula: see text]. The Crowley–Martin response combined with bounded rate of signal production precludes blow-up of solution in model A for [Formula: see text]. Local and global stability of a constant coexistence steady state which is stable for the corresponding ordinary differential equation (ODE) and purely diffusive model are studied along with mechanism of Hopf bifurcation for model B when [Formula: see text] exceeds some critical value. In model A, it is shown that prey-taxis may destabilize the coexistence steady state provided [Formula: see text] and [Formula: see text] are big enough. Numerical simulation depicts emergence of complex space-time patterns for both models and indicates existence of solutions to model A which blow-up in finite time for [Formula: see text].

Repulsive chemotaxis and predator evasion in predator–prey models with diffusion and prey-taxis