Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey 07102, USA.
Federated Department of Biological Sciences, New Jersey Institute of Technology & Rutgers University, Newark, New Jersey 07102, USA.
Chaos. 2022 Jun;32(6):063137. doi: 10.1063/5.0079198.
Several distinct entrainment patterns can occur in the FitzHugh-Nagumo (FHN) model under external periodic forcing. Investigating the FHN model under different types of periodic forcing reveals the existence of multiple disconnected 1:1 entrainment segments for constant, low enough values of the input amplitude when the unforced system is in the vicinity of a Hopf bifurcation. This entrainment structure is termed polyglot to distinguish it from the single 1:1 entrainment region (monoglot) structure typically observed in Arnold tongue diagrams. The emergence of polyglot entrainment is then explained using phase-plane analysis and other dynamical system tools. Entrainment results are investigated for other slow-fast systems of neuronal, circadian, and glycolytic oscillations. Exploring these models, we found that polyglot entrainment structure (multiple 1:1 regions) is observed when the unforced system is in the vicinity of a Hopf bifurcation and the Hopf point is located near a knee of a cubic-like nullcline.
在外部周期性激励下，FitzHugh-Nagumo（FHN）模型中会出现几种不同的同步模式。研究 FHN 模型在不同类型周期性激励下的情况，揭示了当非受迫系统处于 Hopf 分岔附近时，对于足够低的输入幅度的常数，存在多个不连续的 1:1 同步段。这种同步结构被称为多语制，以将其与通常在 Arnold 舌图中观察到的单个 1:1 同步区域（单语制）结构区分开来。然后使用相平面分析和其他动力系统工具来解释多语制同步的出现。还研究了其他神经元、昼夜节律和糖酵解振荡的快慢系统的同步结果。通过探索这些模型，我们发现当非受迫系统处于 Hopf 分岔附近且 Hopf 点位于类似三次样条零值线的拐点附近时，会观察到多语制同步结构（多个 1:1 区域）。
