Intermittent feedback induces attractor selection

Yadav, Kiran; Kamal, Neeraj Kumar; Shrimali, Manish Dev

doi:10.1103/physreve.95.042215

Cited by 21 publications

(10 citation statements)

References 40 publications

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“…Literature provides rich strategies for multistability control (i.e., techniques for annihilating or selecting some stable trajectories among the coexisting ones) including short pulses [37], noise selection [38], harmonic perturbation [39], pseudo-forcing [40], linear augmentation [41] and intermittent feedback [42] to name a few. Except for the two later techniques, practically all other known strategies apply a controller to a single system parameter or state variable.…”

Section: Introductionmentioning

confidence: 99%

“…In some cases, that method alters the monostable survived attractor's intrinsic dynamics. Thankfully, this problem was solved in the relevant work [42], which introduced an intermittent feedback technique for attractor selection. The feedback controller was only turned on when the system was in a specific fraction of state space; otherwise, it was turned off.…”

Section: Introductionmentioning

confidence: 99%

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Coexistence of hyperchaos with chaos and its control in a diode-bridge memristor based MLC circuit with experimental validation

Fozin¹,

Nzoko²,

Telem³

et al. 2022

Phys. Scr.

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This paper reports both the coexistence of chaos and hyperchaos and their control based on a noninvasive temporal feedback method for attractor selection in a multistable non-autonomous memristive Murali-Lakshamanan-Chua (MLC) system. Numerical simulation methods such as bifurcation diagrams, the spectrum of Lyapunov exponents, phase portraits, and cross-section basins of initial states are used to examine several striking dynamical features of the system, including torus, chaos, hyperchaos, and multistability. Of most interest, the rare phenomenon of the coexistence of hyperchaos and chaos has been uncovered based on bifurcation techniques and nonbifurcation scheme like offset boosting. Further analyses based on intermittent feedback-based control in the time domain help to drive the system from the multistable state to a monostable one where only the hyperchaotic attractor survives. Since the attractor's internal dynamics are retained, this control method is non-invasive. At the end of our analyses, the results of both PSpice and that of the microcontroller-based digital calculator of the circuit match perfectly with the numerical investigations.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Coexistence of hyperchaos with chaos and its control in a diode-bridge memristor based MLC circuit with experimental validation

Fozin¹,

Nzoko²,

Telem³

et al. 2022

Phys. Scr.

View full text Add to dashboard Cite

show abstract

“…Since the coexistence of attractors has been commonly used in image processing [16,38], it becomes very urgent to control this phenomenon when, sometimes, periodic and chaotic orbits exist simultaneously. Up to date, the prominent methods reported in the relevant literature which enable to turn a multistable system to a monostable system are the noise selection [39], pseudo-forcing [12], short pulses [40], harmonic perturbation [41], intermittent feedback [42], temporal feedback [43], and linear augmentation [2,3,[44][45][46][47][48][49][50]. Except for the temporal feedback and linear augmentation methods, in almost all other existing methods, the control is applied to one parameter of the system to remove on the attractors for all initial points.…”

Section: Introductionmentioning

confidence: 99%

Control of Coexisting Attractors with Preselection of the Survived Attractor in Multistable Chua’s System: A Case Study

Njitacke

Fozin²,

Tchapga

et al. 2020

Complexity

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Although the control of multistability has already been reported, the one with preselection of the desired attractor is still uncovered in systems with more than two coexisting attractors. This work reports the control of coexisting attractors with preselection of the survived attractors in paradigmatic Chua’s system with smooth cubic nonlinearity. Techniques of linear augmentation combined to system invariant parameters like equilibrium points are used to choose the desired surviving attractors among the coexisting ones. Nonlinear dynamical tools including bifurcation diagrams, standard Lyapunov exponents, phase portraits, and cross section of initial conditions are exploited to reveal the selection scenarios of the survived attractor in the multistability control process of Chua’s system. The main crisis towards annihilation of multistability in Chua’s system when varying the coupling strength is interior crisis and border collision. Theoretical and numerical results obtained are further validated with PSpice analysis.

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“…In fact, positive feedback has been found to favor system instability in dynamical systems and utilized in elevating chaotic behavior and diverging from equilibrium, a scenario that we will be exploring in this work as well. As far as the synchronization and control of networked dynamical systems are concerned, utility of feedback has been well justified [36][37][38][39][40][41][42][43][44][45]. But, the influence of that entity in damaged networks of active (healthy) and inactive (diseased) dynamical systems is yet to be given attention, which is the focus of the present work.…”

Section: Introductionmentioning

confidence: 99%

Resumption of dynamism in damaged networks of coupled oscillators

2018

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Deterioration in dynamical activities may come up naturally or due to environmental influences in a massive portion of biological and physical systems. Such dynamical degradation may have outright effect on the substantive network performance. This requires us to provide some proper prescriptions to overcome undesired circumstances. In this paper, we present a scheme based on external feedback that can efficiently revive dynamism in damaged networks of active and inactive oscillators and thus enhance the network survivability. Both numerical and analytical investigations are performed in order to verify our claim. We also provide a comparative study on the effectiveness of this mechanism for feedbacks to the inactive group or to the active group only. Most importantly, resurrection of dynamical activity is realized even in time-delayed damaged networks, which are considered to be less persistent against deterioration in the form of inactivity in the oscillators. Furthermore, prominence in our approach is substantiated by providing evidence of enhanced network persistence in complex network topologies taking small-world and scale-free architectures, which makes the proposed remedy quite general. Besides the study in the network of Stuart-Landau oscillators, affirmative influence of external feedback has been justified in the network of chaotic Rössler systems as well.

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Intermittent feedback induces attractor selection

Cited by 21 publications

References 40 publications

Coexistence of hyperchaos with chaos and its control in a diode-bridge memristor based MLC circuit with experimental validation

Coexistence of hyperchaos with chaos and its control in a diode-bridge memristor based MLC circuit with experimental validation

Control of Coexisting Attractors with Preselection of the Survived Attractor in Multistable Chua’s System: A Case Study

Resumption of dynamism in damaged networks of coupled oscillators

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