Synchronization of Diffusively Coupled Electronic Hindmarsh-Rose Oscillators

Steur, Erik; Kodde, L.; Nijmeijer, Henk

doi:10.1142/9789814282321_0013

Cited by 7 publications

(3 citation statements)

References 15 publications

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“…In Definition 2.1, we closely follows the stronger notion of practical synchronization from [17] saying that ζ-differences can be made arbitrary small by suitable controls. Note that in our system (2), the magnitude of control terms which are the sinusoidal couplings is dominated by the coupling strength K. In [4,10,12,20,21,22,29], the weaker concepts of practical synchronization comparing the Definition 2.1 were used to denote the uniform boundedness of phase differences in time but no restriction on the bound of the phase differences according to the coupling K. The numerical experiment of [29] shows that large coupling strength is necessary to obtain sufficiently small bound of phase diameter. 2.…”

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confidence: 93%

Practical synchronization of generalized Kuramoto systems with an intrinsic dynamics

Ha¹,

Noh²,

Park³

2015

Networks &Amp; Heterogeneous Media

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We study the practical synchronization of the Kuramoto dynamics of units distributed over networks. The unit dynamics on the nodes of the network are governed by the interplay between their own intrinsic dynamics and Kuramoto coupling dynamics. We present two sufficient conditions for practical synchronization under homogeneous and heterogeneous forcing. For practical synchronization estimates, we employ the configuration diameter as a Lyapunov functional, and derive a Gronwall-type differential inequality for this value.2010 Mathematics Subject Classification. Primary: 70F99; Secondary: 92B25.

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confidence: 93%

Practical synchronization of generalized Kuramoto systems with an intrinsic dynamics

Ha¹,

Noh²,

Park³

2015

Networks &Amp; Heterogeneous Media

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“…We develop and illustrate this training procedure using clusters of neurons of the Hindmarsh-Rose type [Hindmarsh & Rose, 1984] and we verify our results of training using experiments. The experimental setup consists of an epuck mobile robot [Mondada et al, 2009], equipped with the neuronal controller presented in [Wang et al, 2008] with electronic circuit realizations of the Hindmarsh-Rose neuron [Steur et al, 2008;Neefs, 2009;Neefs et al, 2010] as nodes of the neuronal network. We have chosen to use Hindmarsh-Rose model neurons as constituting units as electronic circuit realizations of this model are available to us.…”

Section: Introductionmentioning

confidence: 99%

Training a Network of Electronic Neurons for Control of a Mobile Robot

Vromen

Steur

Nijmeijer

2016

Int. J. Bifurcation Chaos

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An adaptive training procedure is developed for a network of electronic neurons, which controls a mobile robot driving around in an unknown environment while avoiding obstacles. The neuronal network controls the angular velocity of the wheels of the robot based on the sensor readings. The nodes in the neuronal network controller are clusters of neurons rather than single neurons. The adaptive training procedure ensures that the input–output behavior of the clusters is identical, even though the constituting neurons are nonidentical and have, in isolation, nonidentical responses to the same input. In particular, we let the neurons interact via a diffusive coupling, and the proposed training procedure modifies the diffusion interaction weights such that the neurons behave synchronously with a predefined response. The working principle of the training procedure is experimentally validated and results of an experiment with a mobile robot that is completely autonomously driving in an unknown environment with obstacles are presented.

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“…There are different electronic implementations of the Hindmarsh-Rose model [105,144],however, in this Ph.D. Thesis essentially, the electronic design of the Hindmarsh-Rose neuron is based on the work described in the latter reference. Consequently, there are three integrator circuits, which integrate the three state variables of the Hindmarsh-Rose model.…”

Section: Electronic Analysis and Schematicmentioning

confidence: 95%

Synchronization and resonance effects in nonlinear electronic circuits : with neuroscience applications

Vellisca¹,

Alberto²

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Pues bien, a través de esta tesis doctoral el autor acerca aquellos gigantes a una distancia donde más bien parecen de nuestra estatura. En particular, mostrando un pequeño pedazo de un gigantesco campo como es la neurociencia, y cómoéste puede ser modificado simplemente con un "clic" que, como en la vida, marca la diferencia. Velli y MacaAbril 2017."Where there is a will there is a way". Old English Proverb"Shoot for the moon. Even if you miss, you'll land among the stars." Norman Vicent Peale"Life is like riding a bicycle. To keep your balance, you must keep moving."

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Synchronization of Diffusively Coupled Electronic Hindmarsh-Rose Oscillators

Cited by 7 publications

References 15 publications

Practical synchronization of generalized Kuramoto systems with an intrinsic dynamics

Practical synchronization of generalized Kuramoto systems with an intrinsic dynamics

Training a Network of Electronic Neurons for Control of a Mobile Robot

Synchronization and resonance effects in nonlinear electronic circuits : with neuroscience applications

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