On a Predator-Prey System with Random Switching that Never Converges to its Equilibrium

DOI10.1137/18M1196042zbMath1423.92218arXiv1710.01220OpenAlexW2972243378WikidataQ115525592 ScholiaQ115525592MaRDI QIDQ5233765

Alexandru Hening, Edouard Strickler

Publication date: 6 September 2019

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.01220

zbMATH Keywords

Lyapunov exponentspopulation dynamicsLotka-Volterrapiecewise deterministic Markov processesrandom switchingtelegraph noise

Mathematics Subject Classification ID

Population dynamics (general) (92D25) Ordinary differential equations and systems with randomness (34F05) Dynamical systems and their relations with probability theory and stochastic processes (37A50)

Related Items (8)

Random Switching in an Ecosystem with Two Prey and One Predator ⋮ The effects of random and seasonal environmental fluctuations on optimal harvesting and stocking ⋮ A Model of Seasonal Savanna Dynamics ⋮ Quantifying and Managing Uncertainty in Piecewise-Deterministic Markov Processes ⋮ A Method to Deal With the Critical Case in Stochastic Population Dynamics ⋮ Coexistence, extinction, and optimal harvesting in discrete-time stochastic population models ⋮ Stationary distributions of persistent ecological systems ⋮ The competitive exclusion principle in stochastic environments

Cites Work

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• Effect of parity on productivity and sustainability of Lotka-Volterra food chains
• Sensitivity to switching rates in stochastically switched ODEs
• Qualitative properties of certain piecewise deterministic Markov processes
• A piecewise deterministic model for a prey-predator community
• Lotka-Volterra with randomly fluctuating environments or ``how switching between beneficial environments can make survival harder
• Competitive or weak cooperative stochastic Lotka-Volterra systems conditioned on non-extinc\-tion
• Persistence of structured populations in random environments
• Persistence in fluctuating environments
• Random switching between vector fields having a common zero
• Stochastic population growth in spatially heterogeneous environments: the density-dependent case
• Evolution of predator-prey systems described by a Lotka-Volterra equation under random environment
• Comparaison des exposants de Lyapounov des processus markoviens multiplicatifs. (Comparison of Lyapunov exponents of multiplicative Markov processes)
• Persistence in food webs - I. Lotka-Volterra food chains
• General theory of competitive coexistence in spatially-varying environments.
• Stochastic Lotka-Volterra food chains
• Coexistence and extinction for stochastic Kolmogorov systems
• Long term behavior of solutions of the Lotka-Volterra system under small random perturbations.
• Stochastic population growth in spatially heterogeneous environments
• Persistence in stochastic Lotka-Volterra food chains with intraspecific competition
• Decay rates for stabilization of linear continuous-time systems with random switching
• Protected polymorphisms and evolutionary stability of patch-selection strategies in stochastic environments
• On the stability of planar randomly switched systems
• Coexistence in locally regulated competing populations and survival of branching annihilating random walk
• Long-time behaviour of a stochastic prey--predator model.
• Invariant densities for dynamical systems with random switching
• Robust permanence and impermanence for stochastic replicator dynamics
• The Influence of External Real and White Noise on the L<scp>OTKA</scp>‐V<scp>OLTERRA</scp> Model
• Evolutionary Games and Population Dynamics

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