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3D Modeling of Dendritic Spines with Synaptic Plasticity
Published on: May 18, 2020
Modeling synaptic dynamics in neurons via soliton solutions of fractional and stochastic coupled Konno-Oono systems
Musarat Bibi1, Salah Mahmoud Boulaaras2, Muhammad Shoaib Saleem1,3
1Department of Mathematics, University of Okara, Okara, Pakistan.
Abstract:
In this study, we formulate fractional and random extensions of the coupled Konno-Oono system for the dynamics of the neuron circuit. The fractional framework, based on the truncated M-fractional derivative, accounts for memory effects and long-range temporal correlations associated with synaptic plasticity. In contrast, the stochastic component captures synaptic transmission variability arising from ion-channel fluctuations and random neurotransmitter release. Using the Extended Hyperbolic Function Method, various exact soliton solutions are obtained in both the fractional and stochastic models. The obtained results explain the propagation of a localized, stable waveform in neural media under the combined effects of memory and noise. Graphical analyses are presented to illustrate the impact of different fractional orders and noise intensities on the system's dynamical behavior. The proposed formulation offers a unified analytic framework for the investigation of nonlinear propagation of the synapse waves in the complex environment of the neurons.
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