Dynamics of Periodic Waves in a Neural Field Model

Periodic traveling waves are observed in various brain activities, including visual, motor, language, sleep, and so on. There are several neural field models describing periodic waves assuming nonlocal interaction, and possibly, inhibition, time delay or some other properties. In this work we study the influences of asymmetric connectivity functions and of time delay for symmetric connectivity functions on the emergence of periodic waves and their properties. Nonlinear wave dynamics are studied, including modulated and aperiodic waves. Multiplicity of waves for the same values of parameters is observed. External stimulation in order to restore wave propagation in a damaged tissue is discussed.

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Dynamics of Periodic Waves in a Neural Field Model

10.20944/preprints202003.0135.v1 ◽

2020 ◽

Author(s):

Nikolai Bessonov ◽

Anne Beuter ◽

Sergei Trofimchuk ◽

Vitaly Volpert

Keyword(s):

Time Delay ◽

Field Model ◽

Travelling Waves ◽

Neural Field ◽

Nonlocal Interaction ◽

Periodic Waves ◽

External Stimulation ◽

Wave Dynamics ◽

Neural Field Model ◽

Visual Motor

Periodic travelling waves are observed in various brain activities including visual, motor, language, sleep, and so on. There are several neural field models describing periodic waves assuming nonlocal interaction and, possibly, inhibition, time delay, or some other properties. In this work we study the influence of asymmetric connectivity functions and of time delay on the emergence of periodic waves and on their properties. Nonlinear wave dynamics is studied, including modulated and aperiodic waves. Multiplicity of waves for the same values of parameters is observed. External stimulation in order to restore wave propagation in a damaged tissue is discussed.

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Nonlinear analysis of periodic waves in a neural field model

Chaos An Interdisciplinary Journal of Nonlinear Science ◽

10.1063/5.0012010 ◽

2020 ◽

Vol 30 (8) ◽

pp. 083144

Author(s):

S. Budzinskiy ◽

A. Beuter ◽

V. Volpert

Keyword(s):

Nonlinear Analysis ◽

Field Model ◽

Neural Field ◽

Periodic Waves ◽

Neural Field Model

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Boundedness and Stability for Integrodifferential Equations Modeling Neural Field with Time Delay

Neural Computation ◽

10.1162/neco.2007.19.2.570 ◽

2007 ◽

Vol 19 (2) ◽

pp. 570-581 ◽

Cited By ~ 1

Author(s):

Xuyang Lou ◽

Baotong Cui

Keyword(s):

Time Delay ◽

Global Attractor ◽

Field Model ◽

Integrodifferential Equations ◽

Neural Field ◽

Sufficient Condition ◽

Boundedness Condition ◽

Neural Field Model

In this letter, delayed integrodifferential equations modeling neural field (DIEMNF) is studied. The model of DIEMNF is first established as a modified neural field model. Second, it has been proved that if the interconnection of neural field is symmetric, then every trajectory of the system converges to an equilibrium. The boundedness condition for integrodifferential equations modeling neural field with delay is obtained. Moreover, when the interconnection is asymmetric, we give a sufficient condition that can guarantee that the equilibrium of the DIEMNF is unique and is also a global attractor.

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