16 problems

Supertransient-scaling conjecture. As

Riddled-basin conjecture. The basins eventually become riddled as

Let $\Omega=\\{\omega_1,\cdots,\omega_N\\}\in \mathbb{R}^N$ be a fixed frequency vector. Let $\kappa_{\mathrm{c}}(\Omega)$ denote the critical coupling strength for existence of an…

Let $\Omega=\\{\omega_1,\cdots,\omega_N\\}\in \mathbb{R}^N$ be a frequency vector, and let $\Theta^0=\\{\theta_1^0,\cdots,\theta_N^0\\}$ be an initial phase vector. Define the crit…

Quasi-bursting topology conjecture. This dynamical phase may only be realized in local lattice topologies where the cooperative effect of “destructive interference” does not signif…

Let $\Gamma(t)$ be the global Kuramoto order parameter. An oscillator glass is the proposed glass-like state arising in a system of oscillators with random frustrated interactions…

The model considered is a system of heterogeneous Abelian Kuramoto oscillators with random or frustrated interactions, in which attractive and repulsive couplings can produce a vol…

Consider a general $(N,m)$-graph with maximally-active fixed points, meaning fixed points with the largest number of active nodes. When $N=p \mod (m+1)$ with $p\neq 0,1$, all maxim…

The paper studies heteroclinic cycles in rings of coupled oscillators, whose invariant subspaces can produce robust attracting dynamics and non-ergodic behaviour. Typicality conjec…

Locally invariant manifold conjecture. Locally invariant manifolds of this type do indeed exist, and the resulting dynamics includes complex interactions between oscillators.

Consider $n$ oscillators that are weakly interacting with all the other $n-1$ oscillators. Symmetric phase-locking conjecture. The oscillators will reach a final state with mutual…

Mixed connectivity–heterogeneity conjecture. To obtain sharp closed-form synchronization tests for coupled oscillators, one should focus on mixed measures of the network's connecti…

Daido's conjecture. Such frustrated oscillator arrays could potentially behave like spin glasses.

A weak chimera is a state in a coupled population of phase oscillators in which some dynamically coherent groups have different mean frequencies. Typical weak chimeras conjecture.…

The model considers a network of pulse-coupled oscillators with phases $x_k$ and order parameter … where $P=1$ denotes synchronous oscillation and smaller values measure desynchron…

Consider a chain of coupled phase oscillators, with detuning of the end-point oscillators and coupling between neighboring oscillators. Phase-slipping propensity conjecture. Making…