Controlling birhythmicity in a self-sustained oscillator by time-delayed feedback

Ghosh, Pushpita; Sen, Shrabani; Riaz, Syed Shahed; Ray, Deb Shankar

doi:10.1103/physreve.83.036205

Cited by 65 publications

(35 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Only a few works are reported on the control of birhythmicity. Ghosh et al 17 showed that time delay feedback control, which was originally proposed by Pyragas 18 to control chaos, is able to control birhythmicity as well in a modified birhythmic van der Pol oscillator. However, owing to the presence of time delay in their control scheme, a detailed bifurcation analysis for the controlled system is a difficult task.…”

Section: Introductionmentioning

confidence: 99%

Control of birhythmicity: A self-feedback approach

Biswas

Banerjee

Kurths

2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

Control of birhythmicity: A self-feedback approach

Biswas

Banerjee

Kurths

2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

show abstract

“…Extending van der Pol oscillator model with a nonlinear function of higher order polynomial, Kaiser(15;16;36;37;38;39;17;40) has described bi-rythmicity with the nonlinear equation,…”

Section: Three-cycles Case: Kaiser Bi-rythmicity Modelmentioning

confidence: 99%

Reduction of Kinetic Equations to Liénard–Levinson–Smith Form: Counting Limit Cycles

Saha

Gangopadhyay

Ray

2019

Int. J. Appl. Comput. Math

Self Cite

View full text Add to dashboard Cite

We have presented an unified scheme to express a class of system of equations in two variables into a Liénard -Levinson -Smith(LLS) oscillator form. We have derived the condition for limit cycle with special reference to Rayleigh and Liénard systems for arbitrary polynomial functions of damping and restoring force. Krylov-Boguliubov(K-B) method is implemented to determine the maximum number of limit cycles admissible for a LLS oscillator atleast in the weak damping limit. Scheme is illustrated by a number of model systems with single cycle as well as the multiple cycle cases.

show abstract

“…In the case of self-sustained oscillations, one observes a transition between two stable orbits rather than two points. However, it has been shown that the escape is indeed of the Kramers' type for uncorrelated noise [14,15] even in presence of time delay [16][17][18], and it can be ascribed to the existence of a quasipotential or pseudopotential [19,20]. The quasipotential allows to estimate the energy barriers, and indicates that for most parameters, a single attractor is dominantly stable [14,15], while the other is characterized by a small energy barrier.…”

Section: Introductionmentioning

confidence: 99%

Stochastic bifurcations induced by correlated noise in a birhythmic van der Pol system

Yonkeu

Yamapi

Филатрелла

et al. 2016

Communications in Nonlinear Science and Numerical Simulation

View full text Add to dashboard Cite

We investigate the effects of exponentially correlated noise on birhythmic van der Pol type oscillators. The analytical results are obtained applying the quasi-harmonic assumption to the Langevin equation to derive an approximated Fokker-Planck equation. This approach allows to analytically derive the probability distributions as well as the activation energies associated to switching between coexisting attractors. The stationary probability density function of the van der Pol oscillator reveals the influence of the correlation time on the dynamics. Stochastic bifurcations are discussed through a qualitative change of the stationary probability distribution, which indicates that noise intensity and correlation time can be treated as bifurcation parameters. Comparing the analytical and numerical results, we find good agreement both when the frequencies of the attractors are about equal or when they are markedly different.

show abstract

Controlling birhythmicity in a self-sustained oscillator by time-delayed feedback

Cited by 65 publications

References 30 publications

Control of birhythmicity: A self-feedback approach

Control of birhythmicity: A self-feedback approach

Reduction of Kinetic Equations to Liénard–Levinson–Smith Form: Counting Limit Cycles

Stochastic bifurcations induced by correlated noise in a birhythmic van der Pol system

Contact Info

Product

Resources

About