Tagne Nkounga I B, Marwan N, Moukam Kakmeni F M, Yamapi R, Kurths Jürgen
Fundamental Physics Laboratory, Physics of Complex System Group, Department of Physics, Faculty of Science, University of Douala, Box 24 157 Douala, Cameroon.
Potsdam Institute for Climate Impact Research (PIK), Member of the Leibniz Association, Telegraphenberg, P.O. Box 601203, 14473 Potsdam, Germany.
Chaos. 2023 Oct 1;33(10). doi: 10.1063/5.0166691.
In a new memristive generalized FitzHugh-Nagumo bursting model, adaptive resonance (AR), in which the neuron system's response to a varied stimulus can be improved by the ideal intensity of adaptation currents, is examined. We discovered that, in the absence of electromagnetic induction, there is signal detection at the greatest resonance peak of AR using the harmonic balance approach. For electromagnetic induction's minor impacts, this peak of the AR is optimized, whereas for its larger effects, it disappears. We demonstrate dependency on adaption strength as a bifurcation parameter, the presence of period-doubling, and chaotic motion regulated and even annihilated by the increase in electromagnetic induction using bifurcation diagrams and Lyapunov exponents at specific resonance frequencies. The suggested system shows the propagation of localized excitations as chaotic or periodic modulated wave packets that resemble breathing structures. By using a quantitative recurrence-based analysis, it is possible to examine these plausible dynamics in the structures of the recurrence plot beyond the time series and phase portraits. Analytical and numerical analyses are qualitatively consistent.
在一个新的忆阻广义FitzHugh-Nagumo爆发模型中，研究了自适应共振（AR），其中通过适应电流的理想强度可以改善神经元系统对变化刺激的响应。我们发现，在没有电磁感应的情况下，使用谐波平衡方法在AR的最大共振峰处存在信号检测。对于电磁感应的微小影响，AR的这个峰值会被优化，而对于其较大影响，它会消失。我们使用特定共振频率下的分岔图和李雅普诺夫指数，证明了对作为分岔参数的适应强度的依赖性、倍周期的存在以及电磁感应增加对混沌运动的调节甚至消除。所提出的系统显示了局部激发作为类似于呼吸结构的混沌或周期性调制波包的传播。通过基于定量递归的分析，可以在超越时间序列和相图的递归图结构中检查这些合理的动力学。分析和数值分析在定性上是一致的。
