Finite-size scaling in the system of coupled oscillators with heterogeneity in coupling strength

Dynamical phase transitions in the nonreciprocal Ising model

Nonreciprocal interactions in many-body systems lead to time-dependent states, commonly observed in biological, chemical, and ecological systems. The stability of these states in the thermodynamic limit and the critical behavior of the phase transition from static to time-dependent states are not yet fully understood. To address these questions, we study a minimalistic system endowed with nonreciprocal interactions: an Ising model with two spin species having opposing goals. The mean-field equation predicts three stable phases: disorder, static order, and a time-dependent swap phase. Large-scale numerical simulations support the following: (i) in two dimensions, the swap phase is destabilized by defects; (ii) in three dimensions, the swap phase is stable and has the properties of a time crystal; (iii) the transition from disorder to swap in three dimensions is characterized by the critical exponents of the 3D XY model and corresponds to the breaking of a continuous symmetry, time translation invariance; (iv) when the two species have fully antisymmetric couplings, the static-order phase is unstable in any finite dimension due to droplet growth; and (v) in the general case of asymmetric couplings, static order can be restored by a droplet-capture mechanism preventing the droplets from growing indefinitely. We provide details on the full phase diagram, which includes first- and second-order-like phase transitions, and study how the system coarsens into swap and static-order states.

Collective synchronization through noise cancellation

After decades of study, there are only two known mechanisms to induce global synchronization in a population of oscillators: Deterministic coupling and common forcing. The inclusion of independent noise in these models typically serves to drive disorder, increasing the stability of the incoherent state. Here we show that the reverse is also possible. We propose and analyze a simple general model of purely noise coupled oscillators. In the first explicit choice of noise coupling, we find the linear response around incoherence is identical to that of the paradigmatic Kuramoto model but exhibits binary phase locking instead of full coherence. We characterize the phase diagram, stationary states, and approximate low-dimensional dynamics for the model, revealing the curious behavior of this mechanism of synchronization. In the second minimal case we connect the final synchronized state to the initial conditions of the system.

Double resonance induced by group coupling with quenched disorder

Results show that the astrocytes can not only listen to the talk of large assemble of neurons but also give advice to the conversations and are significant sources of heterogeneous couplings as well. In the present work, we focus on such regulation character of astrocytes and explore the role of heterogeneous couplings among interacted neuron-astrocyte components in a signal response. We consider reduced dynamics in which the listening and advising processes of astrocytes are mapped into the form of group coupling, where the couplings are normally distributed. In both globally coupled overdamped bistable oscillators and an excitable FitzHugh-Nagumo (FHN) neuron model, we numerically and analytically demonstrate that two types of bell-shaped collective response curves can be obtained as the ensemble coupling strength or the heterogeneity of group coupling rise, respectively, which can be seen as a new type of double resonance. Furthermore, through the bifurcation analysis, we verify that these resonant signal responses stem from the competition between dispersion and aggregation induced by heterogeneous group and positive pairwise couplings, respectively. Our results contribute to a better understanding of the signal propagation in coupled systems with quenched disorder.

Mean-field analysis of Stuart-Landau oscillator networks with symmetric coupling and dynamical noise

This paper presents analyses of networks composed of homogeneous Stuart-Landau oscillators with symmetric linear coupling and dynamical Gaussian noise. With a simple mean-field approximation, the original system is transformed into a surrogate system that describes uncorrelated oscillation/fluctuation modes of the original system. The steady-state probability distribution for these modes is described using an exponential family, and the dynamics of the system are mainly determined by the eigenvalue spectrum of the coupling matrix and the noise level. The variances of the modes can be expressed as functions of the eigenvalues and noise level, yielding the relation between the covariance matrix and the coupling matrix of the oscillators. With decreasing noise, the leading mode changes from fluctuation to oscillation, generating apparent synchrony of the coupled oscillators, and the condition for such a transition is derived. Finally, the approximate analyses are examined via numerical simulation of the oscillator networks with weak coupling to verify the utility of the approximation in outlining the basic properties of the considered coupled oscillator networks. These results are potentially useful for the modeling and analysis of indirectly measured data of neurodynamics, e.g., via functional magnetic resonance imaging and electroencephalography, as a counterpart of the frequently used Ising model.

Effective and Robust Parameter Identification Procedure of a Two-Site Langmuir Kinetics Model for a Gas Sensor Process

Gas sensors have received plenty of attention due to various applications, and the methods to model the kinetic processes and estimate the corresponding parameters play a critical role in characterizing the sensor response behavior. In this work, a two-site Langmuir kinetics model is applied to describe the adsorption/desorption response processes of a SnO₂/reduced graphene oxide resistive gas sensor and the pertinent kinetic parameters are optimized based on the genetic algorithm (GA). For the robustness and fast convergence of the GA, the initial values and ranges of kinetic parameters are obtained step-by-step. This a priori knowledge is sufficient to guarantee reasonable parameter identification from experimental data. Moreover, the kinetics model and GA are integrated into graphical user interface software for subsequent application. Eventually, the exploration of improvements to experimental design is uncovered to increase the accuracy and reliability of the estimation.