Ensemble Controllability of Cellular Oscillators

Kuritz, Karsten; Zeng, Shen; Allgöwer, Frank

doi:10.1109/lcsys.2018.2870967

Cited by 21 publications

(15 citation statements)

References 38 publications

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“…We will also be able to use the present methods for optimizing mutual synchronization of coupled oscillators. Moreover, though we considered only the optimization of the local linear stability of the phase-locked state, we may be able to the present methods to other optimization problems, such as those for global entrainment property 45 and phase-distribution control [42][43][44][45] . Finally, using the phase-amplitude reduction frameworks for time-delayed 56 and spatially-extended 57 systems, we would also be able to realize fast entrainment in such non-conventional infinite-dimensional systems via amplitude suppression.…”

Section: Discussionmentioning

confidence: 99%

“…The phase equation can also be used to formulate optimization and control problems for limit-cycle oscillators 21 , for example, minimizing the control power [30][31][32][33] , maximizing the locking range [34][35][36] and linear stability 37 in the entrainment, maximizing the linear stability of mutual synchronization between coupled oscillators 38,39 , maximizing the phase coherence of noisy oscillators 40 , performing phase-selective entrainment of oscillators 41 , and controlling the phase distributions in oscillator populations [42][43][44][45] . Optimization methods based on phase reduction have also been studied in non-conventional oscillatory systems such as mutual synchronization between rhythmic spatiotemporal patterns 46 and collectively oscillating networks 47 , and entrainment of a quantum limit-cycle oscillator in the semiclassical regime 48 .…”

Section: Introductionmentioning

confidence: 99%

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Fast optimal entrainment of limit-cycle oscillators by strong periodic inputs via phase-amplitude reduction and Floquet theory

Takata,

Kato,

Nakao

2021

Preprint

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Optimal entrainment of limit-cycle oscillators by strong periodic inputs is studied on the basis of the phase-amplitude reduction and Floquet theory. Two methods for deriving the input waveforms that keep the system state close to the original limit cycle are proposed, which enable the use of strong inputs for entrainment. The first amplitude-feedback method uses feedback control to suppress deviations of the system state from the limit cycle, while the second amplitude-penalty method seeks an input waveform that does not excite large deviations from the limit cycle in the feedforward framework. Optimal entrainment of the Van der Pol and Willamowski-Rössler oscillators with real or complex Floquet exponents are analyzed as examples.It is demonstrated that the proposed methods can achieve much faster entrainment and provide wider entrainment ranges than the conventional method that relies only on phase reduction.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fast optimal entrainment of limit-cycle oscillators by strong periodic inputs via phase-amplitude reduction and Floquet theory

Takata,

Kato,

Nakao

2021

Preprint

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“…where κ = 52. From this we calculate the phase difference distribution from equation (29) or (30), which can then be used to calculate the average synaptic change from equation (32). The bottom left, right, and top right panels of Figure 2 show the desired phase distribution, phase difference distribution, and the product of the phase difference distribution with the STDP curve respectively.…”

Section: Spike Time Dependent Plasticity Stabilizes Clustersmentioning

confidence: 99%

Phase distribution control of a population of oscillators

Monga

Moehlis

2019

Physica D: Nonlinear Phenomena

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The collective behavior of biological oscillators has been recognized as an important problem for several decades, but its control has come into limelight only recently. Much of the focus for control has been on desynchronization of an oscillator population, motivated by the pathological neural synchrony present in essential and parkinsonian tremor. Other applications, such as the beating of the heart and insulin secretion, require synchronization, and recently there has been interest in forming clusters within an oscillator population as well. In this article, we use a formulation that allows us to devise control frameworks to achieve all of these distinct collective behaviors observed in biological oscillators. This is based on the Fourier decomposition of the partial differential equation governing the evolution of the phase distribution of a population of identical, uncoupled oscillators. Our first two control algorithms are Lyapunov-based, which work by decreasing a positive definite Lyapunov function towards zero. Our third control is an optimal control algorithm, which minimizes the control energy consumption while achieving the desired collective behavior of an oscillator population. Motivated by pathological neural synchrony, we apply our control to desynchronize an initially synchronized neural population. Given the proposed importance of enhancing spike time dependent plasticity to stabilize neural clusters and counteract pathological neural synchronization, we formulate the phase difference distribution in terms of the phase distribution, and prove some of its fundamental properties, and in turn apply our control to transform the neural phase distribution to form clusters. Finally, motivated by eliminating cardiac alternans, we apply our control to phase shift a synchronous cardiac pacemaker cell population. For the systems considered in this paper, the control algorithms can be applied to achieve any desired traveling-wave phase distribution, as long as the combination of the initial phase distribution and phase response curve is non-degenerate. To demonstrate the effectiveness of our control for each of these applications, we show that a population of 100 phase oscillators with the applied control mimics the desired phase distribution.

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“…Using the phase equation, we can also formulate optimization and control of nonlinear oscillators [21], for example, minimizing the power for control of oscillators [22][23][24][25], maximizing the range [26][27][28][29] or linear stability [30] of entrainment for periodically forced oscillators, maximizing linear stability of mutual synchronization between two coupled oscillators [31,32], maximizing phase coherence of noisy oscillators [33], phase-selective entrainment of oscillators [34], control of phase distributions in oscillator populations [35,36], and optimizing entrainment stability of quantum limit-cycle oscillators in the semiclassical regime [37].…”

Section: Introductionmentioning

confidence: 99%

Optimization of periodic input waveforms for global entrainment of weakly forced limit-cycle oscillators

Kato,

Zlotnik,

et al. 2021

Preprint

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Ensemble Controllability of Cellular Oscillators

Cited by 21 publications

References 38 publications

Fast optimal entrainment of limit-cycle oscillators by strong periodic inputs via phase-amplitude reduction and Floquet theory

Fast optimal entrainment of limit-cycle oscillators by strong periodic inputs via phase-amplitude reduction and Floquet theory

Phase distribution control of a population of oscillators

Optimization of periodic input waveforms for global entrainment of weakly forced limit-cycle oscillators

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