Control of Hopf Bifurcation and Chaos in a Delayed Lotka-Volterra Predator-Prey System with Time-Delayed Feedbacks

Zhao, Huitao; Sun, Yuangong; Wang, Zhen

doi:10.1155/2014/104156

Cited by 5 publications

(4 citation statements)

References 19 publications

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“…gLV models lack dynamics that occur with the accumulation and depletion of extracellular species, which can be important for predicting the true dynamics of a community [ 13 ]. Modified Lotka-Volterra equations produce chaotic behaviour in predator-prey systems by including time-delayed feedback [ 13 , 14 ], or in one predator two prey systems, by adding dampening effects [ 15 ]. While these abstractions are suitable in some circumstances, by modelling the intermediates involved in competitive interactions we can include experimentally measurable mechanisms and parameters.…”

Section: Introductionmentioning

confidence: 99%

Chaos in synthetic microbial communities

Karkaria

Manhart²,

Fedorec³

et al. 2022

PLoS Comput Biol

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Predictability is a fundamental requirement in biological engineering. As we move to building coordinated multicellular systems, the potential for such systems to display chaotic behaviour becomes a concern. Therefore understanding which systems show chaos is an important design consideration. We developed a methodology to explore the potential for chaotic dynamics in small microbial communities governed by resource competition, intercellular communication and competitive bacteriocin interactions. Our model selection pipeline uses Approximate Bayesian Computation to first identify oscillatory behaviours as a route to finding chaotic behaviour. We have shown that we can expect to find chaotic states in relatively small synthetic microbial systems, understand the governing dynamics and provide insights into how to control such systems. This work is the first to query the existence of chaotic behaviour in synthetic microbial communities and has important ramifications for the fields of biotechnology, bioprocessing and synthetic biology.

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Section: Introductionmentioning

confidence: 99%

Chaos in synthetic microbial communities

Karkaria

Manhart²,

Fedorec³

et al. 2022

PLoS Comput Biol

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show abstract

“…gLV models lack dynamics that occur with the accumulation and depletion of extracellular species, which can be important for predicting the true dynamics of a community [13]. Modified Lotka-Volterra equations produce chaotic behaviour in predator-prey systems by including time-delayed feedback [14, 13], or in one predator two prey systems, by adding dampening effects [15]. While these abstractions are suitable in some circumstances, using them to inform gene regulation networks and community design can be difficult.…”

Section: Introductionmentioning

confidence: 99%

Chaos in small microbial communities

Karkaria

Manhart

Fedorec

et al. 2021

Preprint

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Predictability is a fundamental requirement in biological engineering. As we move to building coordinated multicellular systems, the potential for such systems to display chaotic behaviour becomes a concern. Therefore understanding which systems show chaos is an important design consideration. We developed a methodology to explore the potential for chaotic dynamics in small microbial communities governed by resource competition, intercellular communication and competitive bacteriocin interactions. We show that we can expect to find chaotic states in relatively small synthetic microbial systems, understand the governing dynamics and provide insights into how to control such systems. This work is the first to query the existence of chaotic behaviour in synthetic microbial communities and has important ramifications for the fields of biotechnology, bioprocessing and synthetic biology.

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“…The control of chaos involves eliminating and restraining the chaos phenomenon when it is unavailable and harmful. It has been noticed that purposeful control of chaos can be a key issue in many technological applications [12][13][14][15]. Generally, the existing chaos control methods can be divided into two categories, feedback control and non-feedback control, according to their characteristics.…”

Section: Introductionmentioning

confidence: 99%

Hopf bifurcation and chaos control for a Leslie–Gower type generalist predator model

Chen

Gao

2019

Adv Differ Equ

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This paper is concerned with chaos control and bifurcations of the Leslie-Gower type generalist predator model in a tri-trophic food web system with the time-delayed feedback control. First, the distribution of the roots of the related characteristic equations is analyzed by the polynomial theorem, the conditions to guarantee the existence of Hopf bifurcation are given by choosing the time delay as a bifurcation parameter. Then, the explicit formula for direction of Hopf bifurcation and stability of periodic solutions bifurcating are determined by using the normal form theory and center manifold theorem. Finally, the correctness of our theoretical analysis is verified by some numerical simulation.

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Control of Hopf Bifurcation and Chaos in a Delayed Lotka-Volterra Predator-Prey System with Time-Delayed Feedbacks

Cited by 5 publications

References 19 publications

Chaos in synthetic microbial communities

Chaos in synthetic microbial communities

Chaos in small microbial communities

Hopf bifurcation and chaos control for a Leslie–Gower type generalist predator model

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