Energy balance in feedback synchronization of chaotic systems

Sarasola, C.; Torrealdea, Francisco; D’Anjou, Alicia; Moujahid, Abdelmalik; Graña, Manuel

doi:10.1103/physreve.69.011606

Cited by 98 publications

(47 citation statements)

References 17 publications

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“…Following previous works of finding energy functions of neuron models of chaotic dynamics (Sarasola et al, 2004, 2005; Torrealdea et al, 2009), we have deduced for the model given by Equation (1) an energy function representing the analytical expression of the electrochemical energy involved in its dynamics. The procedure followed to find this energy has been reported in detail in Moujahid et al (2011), and is summarized below.…”

Section: Methodsmentioning

confidence: 99%

Metabolic efficiency with fast spiking in the squid axon

Moujahid¹,

D’Anjou²

2012

Front. Comput. Neurosci.

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Fundamentally, action potentials in the squid axon are consequence of the entrance of sodium ions during the depolarization of the rising phase of the spike mediated by the outflow of potassium ions during the hyperpolarization of the falling phase. Perfect metabolic efficiency with a minimum charge needed for the change in voltage during the action potential would confine sodium entry to the rising phase and potassium efflux to the falling phase. However, because sodium channels remain open to a significant extent during the falling phase, a certain overlap of inward and outward currents is observed. In this work we investigate the impact of ion overlap on the number of the adenosine triphosphate (ATP) molecules and energy cost required per action potential as a function of the temperature in a Hodgkin–Huxley model. Based on a recent approach to computing the energy cost of neuronal action potential generation not based on ion counting, we show that increased firing frequencies induced by higher temperatures imply more efficient use of sodium entry, and then a decrease in the metabolic energy cost required to restore the concentration gradients after an action potential. Also, we determine values of sodium conductance at which the hydrolysis efficiency presents a clear minimum.

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Section: Methodsmentioning

confidence: 99%

Metabolic efficiency with fast spiking in the squid axon

Moujahid¹,

D’Anjou²

2012

Front. Comput. Neurosci.

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“…Identical systems reach complete synchronization spontaneously beyond a given value of the coupling strength and the energy required to maintain this completely synchronized regime is zero. However, between non-identical systems complete synchronization never occurs spontaneously without cost and an average nonzero flow of energy is required to maintain a completely synchronized regime [1]. In this work we investigate, in terms of energy consumption, how an efficient degree of synchronization between two non-identical electrically coupled Hindmarsh-Rose neurons can be reached.…”

Section: Introductionmentioning

confidence: 99%

Efficient synchronization of structurally adaptive coupled Hindmarsh–Rose neurons

Moujahid¹,

D’Anjou²,

Torrealdea³

2011

Chaos, Solitons & Fractals

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The use of spikes to carry information between brain areas implies complete or partial synchronization of the neurons involved. The degree of synchronization reached by two coupled systems and the energy cost of maintaining their synchronized behaviour is highly dependent on the nature of the systems. For non-identical systems the maintenance of a synchronized regime is energetically a costly process. In this work, we study conditions under which two non-identical electrically coupled neurons can reach an efficient regime of synchronization at low energy cost. We show that the energy consumption required to keep the synchronized regime can be spontaneously reduced if the receiving neuron has adaptive mechanisms able to bring its biological parameters closer in value to the corresponding ones in the sending neuron.

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“…Once the exchange of energy will be tested for the coupled flap/lag motion, this system should be analysed according to the studies presented by [13,[16][17][18]. Therefore, a theoretical approach of the problem should be carried out, in order to obtain the Hamilton energy and the results reported by the references [13][14][15] should be taken into account.…”

Section: Introductionmentioning

confidence: 99%

“…In this work, the Hamilton energy of the circuit was determined by the Helmholtz's theorem. Sarasola et al [16] presented a method to assign to a chaotic system of known dynamics a function of the phase space variables with the characteristics of energy. It was studied and discussed the flows of energy at different values of the coupling strength for nonidentical synchronization between Chua guided, Rssler and Lorenz systems.…”

Section: Introductionmentioning

confidence: 99%

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Helicopter flap/lag energy exchange study

Castillo-Rivera

Tomás-Rodrı́guez

2017

Nonlinear Dyn

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This is the accepted version of the paper.This version of the publication may differ from the final published version. Abstract This paper presents a study on the energy exchange taking place on articulated helicopter main rotor blades. The blades are hinged and the flap/lag modes are highly coupled. These dynamical couplings existing between the two degrees of freedom are clearly identifiable as the nonlinear terms that appear in the equations of motion, are key to understand the energy exchange process. The work here conducted is carried out using VehicleSim, a multibody software specialized in modelling mechanical systems composed by rigid bodies. A spring pendulum system is also studied in order to examine its nonlinear behaviour, and to establish existing analogies with the rotor blade nonlinear dynamics. The nonlinear couplings of both systems are compared to each other, and commensurability condition is analysed by means of Short Time Fourier Transform (STFT) methods as well as the flap and lag amplitudes spectrum. Simulations are carried out and the obtained results show clear analogies in the energy exchange process taking place in both systems. The stability of these modes is also studied using Poincare' map method. Permanent repository link

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Energy balance in feedback synchronization of chaotic systems

Cited by 98 publications

References 17 publications

Metabolic efficiency with fast spiking in the squid axon

Metabolic efficiency with fast spiking in the squid axon

Efficient synchronization of structurally adaptive coupled Hindmarsh–Rose neurons

Helicopter flap/lag energy exchange study

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