Control of multistability

Pisarchik, Alexander N.; Feudel, Ulrike

doi:10.1016/j.physrep.2014.02.007

Cited by 694 publications

(333 citation statements)

References 277 publications

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“…Birhythmicity is a variant of multistability, 1 which arises in many natural and artificial systems in the field of physics, 2 biology, [3][4][5] and chemistry. 6 The coexistence of two stable limit cycles of different amplitudes (and frequencies) separated by an unstable limit cycle is the signature of birhythmicity.…”

Section: Introductionmentioning

confidence: 99%

Control of birhythmicity: A self-feedback approach

Biswas

Banerjee

Kurths

2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Birhythmicity occurs in many natural and artificial systems. In this paper, we propose a selffeedback scheme to control birhythmicity. To establish the efficacy and generality of the proposed control scheme, we apply it on three birhythmic oscillators from diverse fields of natural science, namely, an energy harvesting system, the p53-Mdm2 network for protein genesis (the OAK model), and a glycolysis model (modified Decroly-Goldbeter model). Using the harmonic decomposition technique and energy balance method, we derive the analytical conditions for the control of birhythmicity. A detailed numerical bifurcation analysis in the parameter space establishes that the control scheme is capable of eliminating birhythmicity and it can also induce transitions between different forms of bistability. As the proposed control scheme is quite general, it can be applied for control of several real systems, particularly in biochemical and engineering systems. Multistability appears in diverse forms, and their study is an exciting topic of research in science and engineering. A particular form of multistability is bistability: it shows many variants, such as the coexistence of two stable steady states (SSS), one stable steady state and one stable limit cycle (LC), two stable limit cycles, or two chaotic attractors. Birhythmicity is the phenomenon of coexistence of two stable limit cycles separated by an unstable limit cycle with different amplitudes and frequencies. In many physical systems, birhythmicity is undesirable as in energy harvesting systems, but in most biological systems, e.g., enzymatic oscillations, it is desirable. Therefore, control of birhythmicity is of utmost importance. Although the control of multistability is a well studied topic, the control of birhythmicity has not been explored to that extent. In this paper, we propose a control scheme that can effectively control and, whenever required, can eliminate birhythmicity. We theoretically explore and numerically establish the technique of control of birhythmicity and transitions to any desired attractor. A number of engineering and biological systems are investigated with the proposed control scheme to establish the efficacy and generality of the scheme. The main essence of this control scheme lies in the fact that it is easily realizable and offers an efficient mean to control birhythmicity.

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Section: Introductionmentioning

confidence: 99%

Control of birhythmicity: A self-feedback approach

Biswas

Banerjee

Kurths

2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…даже в области параметров, где равновесие популяции устойчиво, существует подобласть, в которой наряду с этим равновесием появляется еще устойчивый аттрактор -цикл длины три. Следует отметить, что возможность одновременного существования в области [31,32].…”

Section: исследование модели на локальную устойчивостьunclassified

Changing the Dynamic Modes in Populations with Short Life Cycle: Mathematical Modeling and Simulation

Фрисман¹,

Frisman²

2014

Math.Biol.Bioinf.

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Аннотация. В простой математической модели динамики популяции обнаружено явление мультирежимности, заключающееся в возможности существования при одних и тех же значениях параметров различных динамических режимов, переход к которым определяется начальными значениями численностей. Данный эффект возникает в модели, имеющей одновременно несколько различных предельных режимов (аттракторов): положение равновесия, регулярные колебания, хаотический аттрактор. Обнаруженное явление мультирежимности позволяет объяснить как возникновение колебаний, так и исчезновение флуктуаций. Адекватность модельных динамических режимов иллюстрируется путем сопоставления их с реальной динамикой численности популяции рыжей полевки (Myodes glareolus). Показано, что влияние внешних климатических факторов на процессы воспроизводства популяции заметно расширяет диапазон возможных динамических режимов и приводит, фактически, к случайному блужданию по бассейнам притяжения этих режимов. Ключевые слова: популяционная динамики, плотностно-зависимая регуляция, математическое моделирование, мультистабильность, мультирежимность, бифуркации, аттрактор, бассейны притяжения. ВВЕДЕНИЕФлуктуации численности популяций у видов с коротким жизненным циклом, особенно мелких млекопитающих (мышевидные грызуны), продолжают оставаться одним из наиболее интересных и загадочных экологических феноменов. Исследования, посвященные изучению механизмов, ведущих к колебательным режимам динамики численности популяций, имеют достаточно долгую историю. Одна из первых работ, в которой был проведен анализ натурных данных численности популяций и выявлено наличие циклических изменений, принадлежит Чарльзу Элтону [1]. К настоящему времени в области изучения популяционных флуктуаций накоплен значительный объем информации по популяционной динамике и разработан ряд теорий, объясняющих механизмы флуктуирующего поведения [2][3][4][5][6][7][8]. Однако ни одна из предложенных концепций не является общепризнанной. Вследствие этого, *

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“…Multistability is an inherent property referring to the systems that exhibit coexistence of several stable solutions for a given set of parameters, and the development of robust control methods based on this feature is a topic of ongoing investigation (see, e.g., [1,2]). Multistability introduces a twofold effect in engineering systems.…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, coexistence of several stable solutions offers great flexibility in the performance of engineering systems, because the system behavior can be changed without altering its major control parameters. For this reason, a significant amount of effort has been dedicated to the development of control strategies that allow judiciously switching between stable solutions in a multistable dynamical scenario; see, e.g., [1,5,6] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

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Controlling multistability in a vibro-impact capsule system

Liu

Chávez

2017

Nonlinear Dyn

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This work concerns the control of multistability in a vibro-impact capsule system driven by a harmonic excitation. The capsule is able to move forward and backward in a rectilinear direction, and the main objective of this work is to control such motion in the presence of multiple coexisting periodic solutions. A position feedback controller is employed in this study, and our numerical investigation demonstrates that the proposed control method gives rise to a dynamical scenario with two coexisting solutions, corresponding to forward and backward progression. Therefore, the motion direction of the system can be controlled by suitably perturbing its initial conditions, without altering the system parameters. To study the robustness of this control method, we apply numerical continuation methods in order to identify a region in the parameter space in which the proposed controller can be applied. For this purpose, we employ the MATLAB-based numerical platform COCO, which

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Control of multistability

Cited by 694 publications

References 277 publications

Control of birhythmicity: A self-feedback approach

Control of birhythmicity: A self-feedback approach

Changing the Dynamic Modes in Populations with Short Life Cycle: Mathematical Modeling and Simulation

Controlling multistability in a vibro-impact capsule system

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