Generalizing the Keller–Segel Model: Lyapunov Functionals, Steady State Analysis, and Blow-Up Results for Multi-species Chemotaxis Models in the Presence of Attraction and Repulsion Between Competitive Interacting Species
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Summary
The famous Keller–Segel model for the chemotactic movement of motile species is extended to some multi-species chemotaxis equations and some interaction effects that have not been studied before are considered.
- Type
- article
- Published
- 2011-04-01
- Cited by
- 177
- References
- 38
- OpenAlex
- https://openalex.org/W2038798727
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:22083172
Keywords
Chemotaxis, Attraction, Steady state (chemistry), Lyapunov function, Stability (learning theory)
References
- Analysis of a Chemotaxis Model for Multi-Species Host-Parasitoid Interactions
- On multivortex solutions in Chern-Simons gauge theory
- LOCAL AND NORM BEHAVIOR OF BLOWUP SOLUTIONS TO A PARABOLIC SYSTEM OF CHEMOTAXIS
- Volume-filling and quorum-sensing in models for chemosensitive movement
- A Non-linear Parabolic System Modeling Chemotaxis with Sensitivity Functions
- Effect of bacterial chemotaxis on dynamics of microbial competition
- Global Behaviour of a Reaction‐Diffusion System Modelling Chemotaxis
- Quantitative studies of bacterial chemotaxis and microbial population dynamics
- Simultaneous finite time blow-up in a two-species model for chemotaxis
- CELLULAR DYNAMICS SIMULATIONS OF BACTERIAL CHEMOTAXIS
- Chemotactic responses to an attractant and a repellent by the polar and lateral flagellar systems of Vibrio alginolyticus.
- A Constructive Approach to Traveling Waves in Chemotaxis
- EQUILIBRIUM OF TWO POPULATIONS SUBJECT TO CHEMOTAXIS
- Stationary solutions of chemotaxis systems
- Coexistence with Chemotaxis
- Model for chemotactic bacterial bands
- On convergence to equilibria for the Keller–Segel chemotaxis model
- "Decision"-Making in Bacteria: Chemotactic Response of Escherichia coli to Conflicting Stimuli
- Initiation of slime mold aggregation viewed as an instability.
- Common Mechanism for Repellents and Attractants in Bacterial Chemotaxis
Cited by
- Chemotactic systems in the presence of conflicts: a new functional inequality
- Part I: Steady States in Two-Species Particle Aggregation; Part II: Sparse Representations For Multiscale PDE
- Analysis of a chemotaxis system modeling ant foraging
- Systèmes d'équations aux dérivées partielles pour la biologie : modèles, analyse numérique et simulations
- Stabilization in a two-species chemotaxis system with a logistic source
- Qualitative analysis of stationary Keller–Segel chemotaxis models with logistic growth
- Global existence of solutions for a fully parabolic chemotaxis system with consumption of chemoattractant and logistic source
- Quasi-gradient systems, modulational dichotomies, and stability of spatially periodic patterns
- Time-periodic and stable patterns of a two-competing-species Keller-Segel chemotaxis model: Effect of cellular growth
- An attraction‐repulsion chemotaxis system with logistic source
- A meeting point of entropy and bifurcations in cross-diffusion herding†
- Do some chemotaxis-growth models possess Lyapunov functionals?
- A Chemotactic Model for Interaction of Antagonistic Microflora Colonies: Front Asymptotics and Numerical Simulations
- Well-posedness for chemotaxis dynamics with nonlinear cell diffusion
- Global existence and asymptotic properties of the solution to a two-species chemotaxis system
- Self-organized populations interacting under pursuit-evasion dynamics
- On a competitive system under chemotactic effects with non-local terms
- Global bounded solutions and their asymptotic properties under small initial data condition in a two-dimensional chemotaxis system for two species
- A Mathematical Characterization for Patterns of a Keller-Segel Model with a Cubic Source Term
- Global boundedness of solutions to a two-species chemotaxis system
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