SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 4, Page 2829-2846, January 2020.
Progression through different synchronized and desynchronized regimes in brain networks has been reported to reflect physiological and behavioral states, such as working memory and attention. Moreover, intracranial recordings of epileptic seizures show a progression towards synchronization as brain regions are recruited and the seizures evolve. In this paper, we build on our previous work on noise- induced transitions on networks to explore the interplay between transitions and synchronization. We consider a bistable dynamical system that is initially at a stable equilibrium (quiescent) that coexists with an oscillatory state (active). The addition of noise will typically lead to escape from the quiescent to the active state. If a number of such systems are coupled, these escapes can spread sequentially in the manner of a “domino effect.” We illustrate our findings numerically in an example system with three coupled nodes. We first show that a symmetrically coupled network with amplitude-dependent coupling exhibits new phenomena of accelerating and decelerating domino effects modulated by the strength and sign of the coupling. This is quantified by numerically computing escape times for the system with weak coupling. We then apply phase-amplitude-dependent coupling and explore the interplay between synchronized and desynchronized dynamics in the system. We consider escape phases between nodes where the cascade of noise-induced escapes is associated with various types of partial synchrony along the sequence. We show examples for the three-node system in which there is multistability between in-phase and antiphase solutions where solutions switch between the two as the sequence of escapes progresses.

中文翻译：

---

双稳态振荡节点网络的顺序转义和同步中断

SIAM应用动力系统杂志，第19卷，第4期，第2829-2846页，2020年1月。
据报道，通过大脑网络中不同同步和不同步状态的进展反映了生理和行为状态，例如工作记忆和注意力。此外，癫痫性癫痫发作的颅内记录显示，随着大脑区域的募集和癫痫发作的发展，同步性逐渐发展。在本文中，我们以我们先前在网络上由噪声引起的过渡上的工作为基础，以探索过渡与同步之间的相互作用。我们考虑一个双稳态动力学系统，该系统最初处于与振动状态（活动状态）共存的稳定平衡状态（静止状态）。噪声的添加通常会导致从静态逃逸到激活状态。如果连接了许多这样的系统，则这些逃逸可以“多米诺效应”的方式顺序扩散。我们在具有三个耦合节点的示例系统中以数字方式说明了我们的发现。我们首先显示具有依赖于幅度的耦合的对称耦合网络展示了由耦合的强度和符号调制的加速和减速多米诺效应的新现象。这可以通过数值计算弱耦合系统的逃逸时间来量化。然后，我们应用依赖于相位振幅的耦合，并探索系统中同步和不同步动力学之间的相互作用。我们考虑节点之间的逃逸阶段，其中噪声诱发的逃逸的级联与沿序列的各种类型的部分同步相关。