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For the high-dimensional Kuramoto model with identical oscillators under a general digraph that has a directed spanning tree, although exponential synchronization was proved under some initial state constraints, the exact exponential synchronization rate has not been revealed until now. In this paper, the exponential synchronization rate is precisely determined as the smallest non-zero real part of Laplacian eigenvalues of the digraph. Our obtained result extends the existing results from the special case of strongly connected balanced digraphs to the condition of general digraphs owning directed spanning trees, which is the weakest condition for synchronization from the aspect of network structure. Moreover, our adopted method is completely different from and much more elementary than the previous differential geometry method.
We study the Kuramoto-Sakaguchi (KS) model composed by any N identical phase oscillators symmetrically coupled. Ranging from local (one-to-one, R = 1) to global (all-to-all, R = N/2) couplings, we derive the general solution that describes the networ
The dynamical behavior of a star network of spins, wherein each of N decoupled spins interact with a central spin through non uniform Heisenberg XX interaction is exactly studied. The time-dependent Schrodinger equation of the spin system model is so
The transient stability of power systems and synchronization of non-uniform Kuramoto oscillators are closely related problems. In this paper, we develop a novel regional stability analysis framework based on the proposed region-parametrized Lyapunov
We reconsider the effect of indistinguishability on the reduced density operator of the internal degrees of freedom (tracing out the spatial degrees of freedom) for a quantum system composed of identical particles located in different spatial regions
We consider the inertial Kuramoto model of $N$ globally coupled oscillators characterized by both their phase and angular velocity, in which there is a time delay in the interaction between the oscillators. Besides the academic interest, we show that