Spatiotemporal complexity of plankton and fish dynamics

AB Medvinsky, SV Petrovskii, IA Tikhonova, H Malchow… - SIAM review, 2002 - SIAM
Nonlinear dynamics and chaotic and complex systems constitute some of the most
fascinating developments of late twentieth century mathematics and physics. The …

Instabilities in spatially extended predator–prey systems: Spatio-temporal patterns in the neighborhood of Turing–Hopf bifurcations

M Baurmann, T Gross, U Feudel - Journal of Theoretical Biology, 2007 - Elsevier
We investigate the emergence of spatio-temporal patterns in ecological systems. In
particular, we study a generalized predator–prey system on a spatial domain. On this …

Wave of chaos: new mechanism of pattern formation in spatio-temporal population dynamics

SV Petrovskii, H Malchow - Theoretical population biology, 2001 - Elsevier
The dynamics of a simple prey–predator system is described by a system of two reaction-
diffusion equations with biologically reasonable non-linearities (logistic growth of the prey …

Pattern formation in prey-taxis systems

JM Lee, T Hillen, MA Lewis - Journal of biological dynamics, 2009 - Taylor & Francis
In this paper, we consider spatial predator–prey models with diffusion and prey-taxis. We
investigate necessary conditions for pattern formation using a variety of non-linear functional …

Influence of isolation degree of spatial patterns on persistence of populations

GQ Sun, ZY Wu, Z Wang, Z Jin - Nonlinear Dynamics, 2016 - Springer
Spatial patterns are ubiquitous in nature, which have been identified as important factors in
dynamics of ecosystems. However, how pattern structures have influence on persistence of …

Directed movement of predators and the emergence of density-dependence in predator–prey models

R Arditi, Y Tyutyunov, A Morgulis, V Govorukhin… - Theoretical population …, 2001 - Elsevier
We consider a bitrophic spatially distributed community consisting of prey and actively
moving predators. The model is based on the assumption that the spatial and temporal …

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

N Sapoukhina, Y Tyutyunov… - The American …, 2003 - journals.uchicago.edu
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 …

[图书][B] Introduction to mathematical modeling and chaotic dynamics

RK Upadhyay, SRK Iyengar - 2013 - books.google.com
Introduction to Mathematical Modeling and Chaotic Dynamics focuses on mathematical
models in natural systems, particularly ecological systems. Most of the models presented are …

A mathematical biologist's guide to absolute and convective instability

JA Sherratt, AS Dagbovie, FM Hilker - Bulletin of mathematical biology, 2014 - Springer
Mathematical models have been highly successful at reproducing the complex
spatiotemporal phenomena seen in many biological systems. However, the ability to …

Modeling the plankton–fish dynamics with top predator interference and multiple gestation delays

NK Thakur, A Ojha, D Jana, RK Upadhyay - Nonlinear Dynamics, 2020 - Springer
Many prey organisms have developed defense mechanisms against predation. If the
predator can encounter in a limited spatial domain, the feeding rates reflect interference …