Related papers: Asymmetry underlies stability in power grids
This work studies the effects of a weak notion of symmetry on diffusively-coupled multi-agent systems. We focus on networks comprised of agents and controllers which are maximally equilibrium independent passive, and show that these…
The contradiction between the fact that many empirical networks possess power-law degree distribution and the finding that network of heterogeneous degree distribution is difficult to synchronize has been a paradox in the study of network…
We analyze networked heterogeneous nonlinear systems, with diffusive coupling and interconnected over a generic static directed graph. Due to the network's hetereogeneity, complete synchronization is impossible, in general, but an emergent…
We present a clear and mathematically simple procedure explaining spontaneous symmetry breaking in quantum mechanical systems. The procedure is applicable to a wide range of models and can be easily used to explain the existence of a…
To understand how certain dynamical behaviors can or cannot persist as the underlying network grows is a problem of increasing importance in complex dynamical systems as well as sustainability science and engineering. We address the…
As bulk synchronous generators in the power grid are replaced by distributed generation interfaced through power electronics, inertia is removed from the system, prompting concerns over grid stability. Different metrics are available for…
The stability of a complex system generally decreases with increasing system size and interconnectivity, a counterintuitive result of widespread importance across the physical, life, and social sciences. Despite recent interest in the…
Symmetries naturally occur in real-world networks and can significantly influence the observed dynamics. For instance, many synchronization patterns result from the underlying network symmetries, and high symmetries are known to increase…
Recent studies have shown that synchronizability of complex networks can be significantly improved by asymmetric couplings, and increase of coupling gradient is always in favor of network synchronization. Here we argue and demonstrate that,…
The fundamental mechanism of transient stability of the conventional power system can be physically understood with the rotor swing dynamics of synchronous generators (SGs). The basic factor affecting the transient stability is the…
The dynamical behavior of networked systems is expected to reflect the features of their coupling structure. Yet, symmetry-broken solutions often occur in symmetrically coupled networks. An example is provided by the so-called solitary…
This paper analyses an emerging real-world phenomena in inverter-based renewable-dominated power systems, namely, asymmetry of frequency distribution. The paper first provides a rationale on why asymmetry reduces the "quality" of the…
Recent research on the network modeling of complex systems has led to a convenient representation of numerous natural, social, and engineered systems that are now recognized as networks of interacting parts. Such systems can exhibit a…
We study the evolution of heterogeneous networks of oscillators subject to a state-dependent interconnection rule. We find that heterogeneity in the node dynamics is key in organizing the architecture of the functional emerging networks. We…
This paper investigates synchronization phenomena in networks of coupled oscillators governed by three-time-scale dynamical systems exhibiting canard dynamics. A mathematical framework has been developed to analyze the synchronization of…
The synchronization of coupled oscillators is a fascinating manifestation of self-organization that nature employs to orchestrate essential processes of life, such as the beating of the heart. Although it was long thought that synchrony or…
Spontaneous symmetry breaking in nonlinear systems provides a unified method to understand vastly different phenomena, ranging from Higgs mechanism [1] and superconductivity [2] to ecological stability [3] and genome generation [4].…
We study explosive synchronization, a phenomenon characterized by first-order phase transitions between incoherent and synchronized states in networks of coupled oscillators. While explosive synchronization has been the subject of many…
Oscillatory dynamics are ubiquitous in biological networks. Possible sources of oscillations are well understood in low-dimensional systems, but have not been fully explored in high-dimensional networks. Here we study large networks…
We present a general theory for the onset of coherence in collections of heterogeneous maps interacting via a complex connection network. Our method allows the dynamics of the individual uncoupled systems to be either chaotic or periodic,…