Soh Guy Blondeau, Tchitnga Robert, Woafo Paul
Laboratory of Electronics, Automation and Signal Processing, Faculty of Science, Department of Physics, University of Dschang, P.O. Box 67, Dschang, Cameroon.
Institute of Surface Chemistry and Catalysis, University of Ulm, Albert-Einstein-Allee 47, 89081 Ulm, Germany.
Heliyon. 2021 May 11;7(5):e07026. doi: 10.1016/j.heliyon.2021.e07026. eCollection 2021 May.
In this paper, analytical and numerical studies of the influence of the long-range interaction parameter on the excitability threshold in a ring of FitzHugh-Nagumo (FHN) system are investigated. The long-range interaction is introduced to the network to model regulation of the Gap junctions or hemichannels activity at the connexins level, which provides links between pre-synaptic and post-synaptic neurons. Results show that the long-range coupling enhances the range of the threshold parameter. We also investigate the long-range effects on the network dynamics, which induces enlargement of the oscillatory zone before the excitable regime. When considering bidirectional coupling, the long-range interaction induces traveling patterns such as traveling waves, while when considering unidirectional coupling, the long-range interaction induces multi-chimera states. We also studied the difference between the dynamics of coupled oscillators and coupled excitable neurons. We found that, for the coupled system, the oscillation period decreases with the increasing of the coupling parameter. For the same values of the coupling parameter, the oscillation period of the Oscillatory dynamics is greater than the oscillation period of the excitable dynamics. The analytical approximation shows good agreement with the numerical results.
本文研究了远程相互作用参数对FitzHugh-Nagumo（FHN）系统环中兴奋性阈值影响的解析和数值研究。将远程相互作用引入网络，以模拟连接蛋白水平上缝隙连接或半通道活性的调节，这为突触前和突触后神经元之间提供了联系。结果表明，远程耦合增强了阈值参数的范围。我们还研究了对网络动力学的远程影响，这会在可兴奋状态之前诱导振荡区域的扩大。当考虑双向耦合时，远程相互作用会诱导出行进模式，如行波，而当考虑单向耦合时，远程相互作用会诱导出多奇异态。我们还研究了耦合振荡器和耦合可兴奋神经元动力学之间的差异。我们发现，对于耦合系统，振荡周期随着耦合参数的增加而减小。对于相同的耦合参数值，振荡动力学的振荡周期大于可兴奋动力学的振荡周期。解析近似与数值结果显示出良好的一致性。
