Optimal entrainment of heterogeneous noisy neurons

Wilson, Dan; Holt, Abbey B.; Netoff, Theoden I.; Moehlis, Jeff

doi:10.3389/fnins.2015.00192

Cited by 30 publications

(15 citation statements)

References 37 publications

(39 reference statements)

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“…Phase reduction has been particularly useful in experimental systems where the full dynamical equations are unknown. For instance, in vitro control applications have been successfully applied to oscillatory neurons [49], [67]. Also, phase response curves have been calculated for melatonin [41] and light [32] in order to determine the phase dependent effect of perturbations to circadian oscillations.…”

Section: Example Of the Direct Methods Applied To A Circadian Systemmentioning

confidence: 99%

Augmented Phase Reduction of (Not So) Weakly Perturbed Coupled Oscillators

Wilson¹,

Ermentrout²

2019

SIAM Rev.

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While phase reduction is a tremendously useful tool for understanding the dynamics of weakly perturbed limit cycle oscillators, its assumptions break down as perturbations become larger, limiting its practical utility in many applications. This fundamental limitation is often apparent when studying coupled populations of oscillators when the collective behavior approaches a limit cycle with transient behavior that decays slowly. Using the notion of isostables of periodic orbits, which define a coordinate system transverse to the limit cycle, we develop a strategy to augment the standard phase reduction in large populations of coupled oscillators to allow for the application of larger perturbations. The resulting augmented phase reduction yields a tremendous decrease in model complexity with a resulting dimensionality that does not depend on the number of oscillators in the population. Additionally, the augmented phase reduction replicates model behavior that standard phase reduction cannot. Finally, we propose and implement a direct method for the application of augmented phase reduction that would be applicable in systems of biological oscillators. Applying the augmented phase reduction to a model of coupled circadian oscillators yields novel insight about the possible mechanism behind the difference in reported jet-lag severity between eastward and westward travel.

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Section: Example Of the Direct Methods Applied To A Circadian Systemmentioning

confidence: 99%

Augmented Phase Reduction of (Not So) Weakly Perturbed Coupled Oscillators

Wilson¹,

Ermentrout²

2019

SIAM Rev.

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“…For example, this occurs in connected vehicle systems where human-driven vehicles are mixed with vehicles of higher levels of autonomy that can exploit wireless vehicle-to-vehicle communication [3]. Similar phenomena can be found when attaching controller genes to gene regulatory networks [26] and when controlling neural ensembles using brain-machine interfaces [27]. In nature, the dynamics of NAAs is often nonlinear.…”

mentioning

confidence: 82%

“…where matrices P i , Q i;j and W i;j are all positive definite for j D 1; : : : ; m i . Substituting (25) and (27) into the time derivative of (56) and adding…”

Section: Appendix B: Proof Of Theoremmentioning

confidence: 99%

Consensus and disturbance attenuation in multi‐agent chains with nonlinear control and time delays

Zhang

Orosz

2016

Int. J. Robust. Nonlinear Control

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In this paper, we investigate consensus and disturbance attenuation in a chain of mobile agents, which include non-autonomous agents, semi-autonomous agents and autonomous agents. In particular, the nonlinear dynamics of non-autonomous agents is given and cannot be designed, while the dynamics of semi-autonomous and autonomous agents can be partially and fully designed, respectively. To improve the robustness of multi-agent chains against disturbances, we propose a nonlinear control framework for semi-autonomous and autonomous agents such that they mimic the behavior of non-autonomous agents for compatibility while also exploiting long-range connections with distant agents. This framework ensures the existence of a unique consensus equilibrium, which is independent of the network size, connectivity topologies, control gains and information delays. Robustness of multi-agent chains against disturbances is investigated by evaluating the frequency response at the nonlinear level. For infinitely long multi-agent chains with recurrent patterns, we also derive a condition that ensures the disturbance attenuation but only requires the analysis of the linearized model. A case study is conducted for a connected vehicle system where numerical simulations are used to validate the analytical results. disturbance is amplified while propagating along the chain of vehicles [14,15]. Disturbance attenuation in undirected networks of agents with identical linear dynamics was investigated in [16], while a distributed H 1 control for network consensus was presented in [17]. For chains of connected and automated vehicles (CAVs), disturbance attenuation is often called 'string stability' and has been widely studied [18][19][20][21][22][23][24][25].The aforementioned studies on disturbance attenuation in networks assumed that the dynamics of all agents can be designed. However, in practice, there may exist non-autonomous agents (NAAs) that follow certain rules based on their own perception so that their dynamics cannot be designed. On the other hand, the dynamics of semi-autonomous (SAAs) and autonomous (AAs) agents may be partially and fully designed, respectively, while they may also exploit long-range interactions with distant agents. For example, this occurs in connected vehicle systems where human-driven vehicles are mixed with vehicles of higher levels of autonomy that can exploit wireless vehicle-to-vehicle communication [3]. Similar phenomena can be found when attaching controller genes to gene regulatory networks [26] and when controlling neural ensembles using brain-machine interfaces [27]. In nature, the dynamics of NAAs is often nonlinear. For compatibility, it is crucial to ensure that the SAAs and AAs follow similar rules as the NAAs. Thus, their controllers need to be nonlinear as well. Moreover, time delays often arise in the information exchange between agents. Distributed nonlinear control for consensus and disturbance attenuation in time-delayed networks that include NAAs is still an open problem.In this paper, we foc...

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“…We note that (1) can be appended to include additional terms such as noise and coupling in a population. Phase reduction has been applied fruitfully to many applications to both understand and control populations of phase oscillators [7], [8], [5], [9], [10], [11]. Essential to the understanding of these oscillatory group dynamics is the ability to accurately compute PRCs, which for systems in silico has been rendered nearly trivial with modern computing algorithms and software [12], [13], [14].…”

Section: Introductionmentioning

confidence: 99%

Determining individual phase response curves from aggregate population data

Wilson

Moehlis

2015

Phys. Rev. E

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Phase reduction is an invaluable technique for investigating the dynamics of nonlinear limit cycle oscillators. Central to the implementation of phase reduction is the ability to calculate phase response curves (PRCs), which describe an oscillator's response to an external perturbation. Current experimental techniques for inferring PRCs require data from individual oscillators, which can be impractical to obtain when the oscillator is part of a much larger population. Here we present a simple yet novel methodology to calculate PRCs of individual oscillators using an aggregate signal from a large homogeneous population. This methodology is shown to be accurate in the presence of inter-oscillator coupling and noise and can also provide a good estimate of an average PRC of a heterogeneous population. We also find that standard experimental techniques for PRC measurement can produce misleading results when applied to aggregate population data.

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Optimal entrainment of heterogeneous noisy neurons

Cited by 30 publications

References 37 publications

Augmented Phase Reduction of (Not So) Weakly Perturbed Coupled Oscillators

Augmented Phase Reduction of (Not So) Weakly Perturbed Coupled Oscillators

Consensus and disturbance attenuation in multi‐agent chains with nonlinear control and time delays

Determining individual phase response curves from aggregate population data

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