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Register a new userExplosive first-order transition to synchrony in networked chaotic oscillators
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Critical phenomena in complex networks, and the emergence of dynamical abrupt transitions in the macroscopic state of the system are currently a subject of the outmost interest. We report evidence of an explosive phase synchronization in networks of chaotic units. Namely, by means of both extensive simulations of networks made up of chaotic units, and validation with an experiment of electronic circuits in a star configuration, we demonstrate the existence of a first order transition towards synchronization of the phases of the networked units. Our findings constitute the first prove of this kind of synchronization in practice, thus opening the path to its use in real-world applications.
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Recently, the explosive phase transitions, such as explosive percolation and explosive synchronization, have attracted extensive research interest. So far, most existing works investigate Kuramoto-type models, where only phase variables are involved. Here, we report the occurrence of explosive oscillation quenching in a system of coupled Stuart-Landau oscillators that incorporates both phase and amplitude dynamics. We observe three typical scenarios with distinct microscopic mechanism of occurrence, i.e., ordinary, hierarchical, and cluster explosive oscillation death, corresponding to different frequency distributions of oscillators, respectively. We carry out theoretical analyses and obtain the backward transition point, which is shown to be independent of the specific frequency distributions. Numerical results are consistent with the theoretical prediction.
Recent years have seen an increasing interest in quantum chaos and related aspects of spatially extended systems, such as spin chains. However, the results are strongly system dependent, generic approaches suggest the presence of many-body localization while analytical calculations for certain system classes, here referred to as the ``self-dual case, prove adherence to universal (chaotic) spectral behavior. We address these issues studying the level statistics in the vicinity of the latter case, thereby revealing transitions to many-body localization as well as the appearance of several non-standard random-matrix universality classes.
In this letter, we demonstrate that a non-Hermitian Random Matrix description can account for both spectral and spatial statistics of resonance states in a weakly open chaotic wave system with continuously distributed losses. More specifically, the statistics of resonance states in an open 2D chaotic microwave cavity are investigated by solving the Maxwell equations with lossy boundaries subject to Ohmic dissipation. We successfully compare the statistics of its complex-valued resonance states and associated widths with analytical predictions based on a non-Hermitian effective Hamiltonian model defined by a finite number of fictitious open channels.
Many biological and chemical systems exhibit collective behavior in response to the change in their population density. These elements or cells communicate with each other via dynamical agents or signaling molecules. In this work, we explore the dynamics of nonlinear oscillators, specifically Stuart-Landau oscillators and Rayleigh oscillators, interacting globally through dynamical agents in the surrounding environment modeled as a quorum sensing interaction. The system exhibits the typical continuous second-order transition from oscillatory state to death state, when the oscillation amplitude is small. However, interestingly, when the amplitude of oscillations is large we find that the system shows an abrupt transition from oscillatory to death state, a transition termed explosive death. So the quorum-sensing form of interaction can induce the usual second-order transition, as well as sudden first-order transitions. Further in case of the explosive death transitions, the oscillatory state and the death state coexist over a range of coupling strengths near the transition point. This emergent regime of hysteresis widens with increasing strength of the mean-field feedback, and is relevant to hysteresis that is widely observed in biological, chemical and physical processes.
We present a computer-assisted approach to coarse-graining the evolutionary dynamics of a system of nonidentical oscillators coupled through a (fixed) network structure. The existence of a spectral gap for the coupling network graph Laplacian suggests that the graph dynamics may quickly become low-dimensional. Our first choice of coarse variables consists of the components of the oscillator states -their (complex) phase angles- along the leading eigenvectors of this Laplacian. We then use the equation-free framework [1], circumventing the derivation of explicit coarse-grained equations, to perform computational tasks such as coarse projective integration, coarse fixed point and coarse limit cycle computations. In a second step, we explore an approach to incorporating oscillator heterogeneity in the coarse-graining process. The approach is based on the observation of fastdeveloping correlations between oscillator state and oscillator intrinsic properties, and establishes a connection with tools developed in the context of uncertainty quantification.
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