We study the dynamics arising when two identical oscillators are coupled near a Hopf bifurcation where we assume a parameter ϵ uncouples the system at $\epsilon =0$ . Using a normal form for $N=2$ identical systems undergoing Hopf bifurcation, we explore the dynamical properties. Matching the normal form coefficients to a coupled Wilson–Cowan oscillator network gives an understanding of different types of behaviour that arise in a model of perceptual bistability. Notably, we find bistability between in-phase and anti-phase solutions that demonstrates the feasibility for synchronisation to act as the mechanism by which periodic inputs can be segregated (rather than via strong inhibitory coupling, as in the existing models). Using numerical continuation we confirm our theoretical analysis for small coupling strength and explore the bifurcation diagrams for large coupling strength, where the normal form approximation breaks down.

中文翻译：

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相同Hopf分叉的解耦极限及其在感知双稳态中的应用。

我们研究了当两个相同的振荡器在Hopf分叉附近耦合时产生的动力学，在这里我们假设参数a在$ \ epsilon = 0 $时使系统解耦。对于正经历Hopf分支的$ N = 2 $个相同系统，使用范式，我们研究了动力学性质。将正常形式系数与耦合的Wilson-Cowan振荡器网络相匹配，可以理解在感知双稳态模型中出现的不同类型的行为。值得注意的是，我们在同相和反相解决方案之间发现了双稳态，这证明了同步作为隔离周期性输入的机制（而不是像现有模型那样通过强抑制性耦合）起作用的可行性。