Stochastic bifurcation and Break-out of dynamic balance of predator-prey system with Markov switching

Wei, Wei; Xu, Wei; Liu, Jiankang; Song, Yi; Zhang, Shuo

doi:10.1016/j.apm.2022.12.034

Cited by 6 publications

(2 citation statements)

References 35 publications

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“…Intraspecific and interspecific interactions are commonly categorized, with interspecific relationships primarily centered around predation, competition, and cooperation. Literature [14] introduced Markov transforms into the predator-feeder model to explore the stochastic bifurcation and dynamic equilibrium in the system, finding quantitative conditions for the smooth distribution and proving that it is more sensitive to the rate of leapfrogging. Literature [15] discusses the equilibrium point of the Lotka-Volterra predator-eater system with Allee's influence, and an iterative method is used to derive the conditions for the infinite time-lag system to be in a positive equilibrium global attractor point, which is verified by numerical simulations.…”

Section: Introductionmentioning

confidence: 99%

A study of periodic solutions of several types of nonlinear models in biomathematics

2024

Applied Mathematics and Nonlinear Sciences

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Biomathematics is a cross-discipline formed by the interpenetration of mathematics with life sciences, biology, and other disciplines, and biomathematical models provide an effective tool for solving problems in the above application areas. Our aim in this paper is to combine mathematical analytical tools and numerical simulation methods to investigate the existence and steady state of periodic solutions in different nonlinear models. Time lags with both discrete and distributed characteristics are introduced into the Lotka-Volterra predator-feeder system, and based on the discussion of the central manifold theorem and canonical type theory, it is proved that the branching periodic solution exists when the discrete time lag parameter τ > τ 0. In the SEIRS infectious disease model with nonlinear incidence term and vertical transmission, the global stability of the disease-free equilibrium point and the local asymptotic stability of the endemic equilibrium point are analyzed through the computation and discussion of the fundamental regeneration number R 0 (p, q). A class of convergence-growth models with nonlinear sensitivity functions is studied, and the global boundedness of classical solutions and their conditions are demonstrated based on global dynamics. A mathematical generalization of the muscular vascular model is made by introducing a centralized parameter, the relationship between periodic solutions and chaotic phenomena is explored utilizing a systematic equivalence transformation, and the equation of the homoscedastic orbitals is deduced to be z 2 = x 2 ( A - 1 2 x 2 ) {z^2} = {x^2}\left( {A - {1 \over 2}{x^2}} \right) .

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Section: Introductionmentioning

confidence: 99%

A study of periodic solutions of several types of nonlinear models in biomathematics

2024

Applied Mathematics and Nonlinear Sciences

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“…13.548832 doi: bioRxiv preprint tions (BKEs), governing the probability laws modeled by the SDEs. Indeed, BKEs have been widely utilized for analyzing probabilistic behaviors of stochastic systems of interest in the science and engineering, such as disease transmission [31], predator-prey dynamics [32], chaotic flows [33], rare events in an active matter [34], and machine learning [35].…”

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confidence: 99%

A jump-driven self-exciting stochastic fish migration model and its fisheries applications

Yoshioka

Yamazaki

2023

Preprint

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We introduce a stochastic continuous-time model via a self-exciting process with jumps to describe a seasonal migration event of diadromous fish. The dynamics of the stored population at a point in a river, waiting for their upward migration, increases by the inflow from the downstream/ocean and decreases by the outflow due to their upstream migration. The inflow is assumed to occur at a constant rate until an Erlang-distributed termination time. The outflow is modeled by a self-exciting jump process to incorporate the flocking and social interactions in fish migration. Harvested cases are also studied for fisheries applications. We derive the backward Kolmogorov equations and the associated finite-difference method to compute various performance indices including the mean migration period and　harvested populations. Detailed numerical and　sensitivity analysis are conducted to study the spring upstream migration of the diadromous Ayu Plecoglossus altivelis altivelis.

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Stochastic Hopf bifurcation and random chaos of the ship rolling dynamic system in random longitudinal wave induced by GWN

Zhou

2023

Ocean Engineering

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Stochastic bifurcation and Break-out of dynamic balance of predator-prey system with Markov switching

Cited by 6 publications

References 35 publications

A study of periodic solutions of several types of nonlinear models in biomathematics

A study of periodic solutions of several types of nonlinear models in biomathematics

A jump-driven self-exciting stochastic fish migration model and its fisheries applications

Stochastic Hopf bifurcation and random chaos of the ship rolling dynamic system in random longitudinal wave induced by GWN

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