Bosco Nívea D, Rech Paulo C, Beims Marcus W, Manchein Cesar
Departamento de Física, Universidade do Estado de Santa Catarina, 89219-710 Joinville, Brazil.
Departamento de Física, Universidade Federal do Paraná, 81531-980 Curitiba, Brazil.
Chaos. 2024 Sep 1;34(9). doi: 10.1063/5.0219640.
In this paper, we investigate a seven-parameter, five-dimensional dynamical system, specifically a unidirectional coupling of two FitzHugh-Nagumo neuron models, with one neuron being sinusoidally driven. This master-slave configuration features neuron N1 as the master, subjected to an external sinusoidal electrical current, and neuron N2 as the slave, interacting with N1 through an electrical force. We report numerical results for three distinct scenarios where N1 operates in (i) periodic, (ii) quasiperiodic, and (iii) chaotic regimes. The primary objective is to explore how the dynamics of the master neuron N1 influence the coupled system's behavior. To achieve this, we generated cross sections of the seven-dimensional parameter space, known as parameter planes. Our findings reveal that in the periodic regime of N1, the coupled system exhibits period-adding sequences of Arnold tongue-like structures in the parameter planes. Furthermore, regions of multistability can also be identified in these parameter planes of the coupled system. In the quasiperiodic regime, regions of periodic motion are absent, with only regions of quasiperiodic and chaotic dynamics present. In the chaotic regime of N1, the parameter planes display regions of chaos, hyperchaos, and transient hyperchaos.
在本文中，我们研究了一个七参数、五维动力系统，具体而言是两个FitzHugh-Nagumo神经元模型的单向耦合，其中一个神经元受到正弦驱动。这种主从配置中，神经元N1为主，受到外部正弦电流作用，神经元N2为从，通过电力与N1相互作用。我们报告了三种不同情况下的数值结果，其中N1分别处于（i）周期、（ii）准周期和（iii）混沌状态。主要目的是探索主神经元N1的动力学如何影响耦合系统的行为。为实现这一目标，我们生成了七维参数空间的横截面，即参数平面。我们的研究结果表明，在N1的周期状态下，耦合系统在参数平面上呈现出类似阿诺德舌状结构的周期增加序列。此外，在耦合系统的这些参数平面中也可以识别出多稳态区域。在准周期状态下，不存在周期运动区域，仅存在准周期和混沌动力学区域。在N1的混沌状态下，参数平面显示出混沌、超混沌和瞬态超混沌区域。
