Pattern formation in diffusive excitable systems under magnetic flow effects

Mvogo, Alain; Takembo, Clovis Ntahkie; Fouda, H. P. Ekobena; Kofané, Timoléon Crépin

doi:10.1016/j.physleta.2017.05.020

Cited by 48 publications

(10 citation statements)

References 29 publications

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“…The result obtained in this work also agrees with experimental observations from cultured cardiac myocyte 34,35 . Spatiotemporal dynamical patterns including the wave pattern obtained in this work in the form of discrete pulses have been reported in excitable network, physical and biological media 24,32,36,38 . Spatiotemporal patterns have been reported in excitable brain micro-circuits, described to be highly relevant in intercellular communication such as visual and olfactory cortices 37 .…”

Section: Spatiotemporal Patterns Under Thermoelectric Couplings the mentioning

confidence: 71%

“…( 17 ) is a well-known model usually encountered 33 . Recently, this model has also been reported in biological media 24 . We build an approximate solution of Eq.…”

Section: Modulaional Instability Analysismentioning

confidence: 78%

“…Indeed, MI is a well known and documented mechanism in nonlinear physics. This ranges from fluid dynamics 22 , Bose Einstein condensate 23 , neurons electrical activities 24 and cardiac action potential dynamics 25 . MI leads to the formation of soliton and wave trains in dynamical system due to the interactive effects of dispersion and nonlinearity.…”

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confidence: 99%

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Effect of temperature fluctuation on the localized pattern of action potential in cardiac tissue

Takembo

Fouda

2020

Sci Rep

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Based on the improved FitzHugh–Nagumo myocardial model driven by a constant external current, the effect of temperature fluctuation in a network of electrically coupled myocardial cells are investigated through analytical and numerical computations. Through the technique of multiple scale expansion, we successfully reduced the complex nonlinear system of equations to a more tractable and solvable nonlinear amplitude equation on which the analysis of linear stability is performed. Interestingly from this analysis, a plot of critical amplitude of action potential versus wave number revealed the growth rate of modulational instability (MI) is an increasing function of the thermoelectric couplings; $$T^{(1)}$$ T ( 1 ) and $$T^{(2)}$$ T ( 2 ) , under fixed conditions of nonlinear electrical couplings. In order to verify our analytical predictions through the study the long-time evolution of the modulated cardiac impulses, numerical computation is finally carried out. Numerical experiment revealed the existence of localized coherent structures with some recognized features of synchronization. Through the mechanism of MI, changes in thermoelectrical couplings promote wave localization and mode transition in electrical activities in the cell lattice. Results could provide new insights in understanding the underlying mechanism of the manifestation of sudden heart disorder subjected to heavily temperature fluctuation.

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Section: Spatiotemporal Patterns Under Thermoelectric Couplings the mentioning

confidence: 71%

“…( 17 ) is a well-known model usually encountered 33 . Recently, this model has also been reported in biological media 24 . We build an approximate solution of Eq.…”

Section: Modulaional Instability Analysismentioning

confidence: 78%

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Effect of temperature fluctuation on the localized pattern of action potential in cardiac tissue

Takembo

Fouda

2020

Sci Rep

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“…Mvogo et al . [15] showed diverse spatiotemporal patterns in the neuronal networks under electromagnetic induction radiation. Thus it was generally observed that the electrical activity and oscillating behaviors of biological cells are greatly reduced due to electromagnetic radiation exposure and which is consistent with biological experiments [16, 17].…”

Section: Introductionmentioning

confidence: 99%

Localized nonlinear excitations in diffusive memristor-based neuronal networks

et al. 2019

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We extend the existing ordinary differential equations modeling neural electrical activity to include the memory effect of electromagnetic induction through magnetic flux, used to describe time varying electromagnetic field. Through the multi-scale expansion in the semi-discrete approximation, we show that the neural network dynamical equations can be governed by the complex Ginzburg-Landau equation. The analytical and numerical envelop soliton of this equation are reported. The results obtained suggest the possibility of collective information processing and sharing in the nervous system, operating in both the spatial and temporal domains in the form of localized modulated waves. The effects of memristive synaptic electromagnetic induction coupling and perturbation on the modulated action potential dynamics examined. Large electromagnetic induction coupling strength may contribute to signal block as the amplitude of modulated waves are observed to decrease. This could help in the development of a chemical brain anaesthesia for some brain pathologies.

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“…Specifically, mode transition is detected and mismatch of frequency between electromagnetic radiation and the system is found (Ma et al, 2017 ). Magnetic flux on membrane potential is realized by a mimristor coupling, which leads to non-linear quasi-periodic spatial-temporal patterns (Mvogo et al, 2017 ).…”

Section: Introductionmentioning

confidence: 99%

A Route to Chaotic Behavior of Single Neuron Exposed to External Electromagnetic Radiation

Feng

Zhang

2017

Front. Comput. Neurosci.

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Non-linear behaviors of a single neuron described by Fitzhugh-Nagumo (FHN) neuron model, with external electromagnetic radiation considered, is investigated. It is discovered that with external electromagnetic radiation in form of a cosine function, the mode selection of membrane potential occurs among periodic, quasi-periodic, and chaotic motions as increasing the frequency of external transmembrane current, which is selected as a sinusoidal function. When the frequency is small or large enough, periodic, and quasi-periodic motions are captured alternatively. Otherwise, when frequency is in interval 0.778 < ω < 2.208, chaotic motion characterizes the main behavior type. The mechanism of mode transition from quasi-periodic to chaotic motion is also observed when varying the amplitude of external electromagnetic radiation. The frequency apparently plays a more important role in determining the system behavior.

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Pattern formation in diffusive excitable systems under magnetic flow effects

Cited by 48 publications

References 29 publications

Effect of temperature fluctuation on the localized pattern of action potential in cardiac tissue

Effect of temperature fluctuation on the localized pattern of action potential in cardiac tissue

Localized nonlinear excitations in diffusive memristor-based neuronal networks

A Route to Chaotic Behavior of Single Neuron Exposed to External Electromagnetic Radiation

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