SPATIAL PATTERN IN A PREDATOR-PREY SYSTEM WITH BOTH SELF- AND CROSS-DIFFUSION

DOI10.1142/S0129183109013467zbMath1155.35476WikidataQ115523965 ScholiaQ115523965MaRDI QIDQ3614041

Quan-Xing Liu, Li Li, Yi-Guo Zhao, Zhen Jin, Gui-Quan Sun

Publication date: 16 March 2009

Published in: International Journal of Modern Physics C (Search for Journal in Brave)

Mathematics Subject Classification ID

PDEs in connection with biology, chemistry and other natural sciences (35Q92) Population dynamics (general) (92D25)

Related Items (27)

Pattern formation and spatiotemporal chaos in a reaction-diffusion predator-prey system ⋮ Bifurcation Analysis and Spatiotemporal Patterns in a Diffusive Predator–Prey Model ⋮ Cross-diffusion-driven Turing instability and weakly nonlinear analysis of Turing patterns in a uni-directional consumer-resource system ⋮ Dynamical Complexity and Numerical Bifurcation Analysis of a ReactionDiffusion Predator-Prey System ⋮ Cross-diffusion-driven instability in an interacting species model with prey refuge ⋮ An analysis of a predator-prey model with both diffusion and migration ⋮ Turing patterns induced by cross-diffusion in a predator-prey system in presence of habitat complexity ⋮ Pattern formation of a spatial predator-prey system ⋮ Dynamic behaviour of a reaction-diffusion predator-prey model with both refuge and harvesting ⋮ Spatiotemporal dynamics of Leslie-Gower predator-prey model with Allee effect on both populations ⋮ Dynamical transition and bifurcation of a diffusive predator-prey model with an Allee effect on prey ⋮ Study of Turing patterns in a SI reaction-diffusion propagation system based on network and non-network environments ⋮ Turing Instability and Pattern Formation in a Strongly Coupled Diffusive Predator–Prey System ⋮ Spatial patterns of a predator-prey model with cross diffusion ⋮ Synchronization and spatial patterns in a light-dependent neural network ⋮ Pattern formation in a semi-ratio-dependent predator-prey system with diffusion ⋮ Persistence and Turing instability in a cross-diffusive predator-prey system with generalist predator ⋮ Spatiotemporal dynamics of a predator-prey system with linear harvesting rate ⋮ Stability and Hopf bifurcation for a delayed diffusive competition model with saturation effect ⋮ Existence of spatial patterns in a predator-prey model with self- and cross-diffusion ⋮ EMERGENCE OF OSCILLATORY TURING PATTERNS INDUCED BY CROSS DIFFUSION IN A PREDATOR–PREY SYSTEM ⋮ Pattern formation of an epidemic model with cross diffusion ⋮ Turing instability in a SIS epidemiological model in discrete space with self and cross migration ⋮ Cross-diffusion induced Turing instability for a competition model with saturation effect ⋮ Turing instability in a diffusive SIS epidemiological model ⋮ Spatiotemporal pattern in a self- and cross-diffusive predation model with the Allee effect ⋮ Spatiotemporal dynamics of an NPZ model with prey-taxis and intratrophic predation

Cites Work

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• A Markov chain analysis of predator strategy in a model-mimic system
• Some results on global stability of a predator-prey system
• Stability analysis of predator-prey models via the Liapunov method
• Global stability in two species interactions
• Graphical stability, enrichment, and pest control by a natural enemy
• Pattern formation and the spatial scale of interaction between predators and their prey
• Diffusion vs cross-diffusion: An elliptic approach
• Global qualitative analysis of a ratio-dependent predator-prey system
• Stability of steady-state solutions to a prey--predator system with cross-diffusion.
• Multiple coexistence states for a prey-predator system with cross-diffusion.
• Diffusion, self-diffusion and cross-diffusion
• Spatiotemporal Complexity of Plankton and Fish Dynamics
• The chemical basis of morphogenesis
• Global Stability for a Class of Predator-Prey Systems
• Bifurcations of a Ratio-Dependent Predator-Prey System with Constant Rate Harvesting
• Simple mathematical models with very complicated dynamics
• Pattern formation outside of equilibrium

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