arXiv subjects

Chunming Zheng

Publications and source records attributed to Chunming Zheng.

9 recordsLinked to original sources

arXiv2026

Mesoscopic theory of flocking with alignment and anti-alignment copying

We study a stochastic model of collective motion in which individuals update their orientation through pairwise aligning or anti-aligning copying interactions. We analyze both annealed dynamics, where interaction types are chosen probabilistically at each update, and quenched dynamics, where individuals are permanently assigned to aligning or anti-aligning subpopulations. Starting from the microscopic master equation on the circle, we derive an exact mesoscopic description via a Fourier-mode expansion and a systematic large $N$ expansion, obtaining closed Fokker-Planck equations and effective stochastic differential equations for the polarization. We show that competing alignment and anti-alignment suppress long-range polar order in the thermodynamic limit in both cases, while finite systems display nontrivial fluctuation-induced structure controlled by the interaction composition. Our results, validated by Gillespie simulations, establish an analytically tractable framework for collective dynamics characterized by competing copying rules and intrinsic noise.

cond-mat.stat-mech↗

arXiv2026

Impact of heavy-tailed synaptic strength distributions on self-sustained activity in networks of spiking neurons

We analyze states of stationary activity in randomly coupled quadratic integrate-and-fire neurons using stochastic mean-field theory. Specifically, we consider the two cases of Gaussian random coupling and Cauchy random coupling, which are representative of systems with light- or with heavy-tailed synaptic strength distributions. For both, Gaussian and Cauchy coupling, bistability between a low activity and a high activity state of self-sustained firing is possible in excitable neurons. In the system with Cauchy coupling we find analytically a directed percolation threshold, i.e., above a critical value of the synaptic strength, activity percolates through the whole network starting from a few spiking units only. The existence of the directed percolation threshold is in agreement with previous numerical results in the literature for integrate-and-fire neurons with heavy-tailed synaptic strength distribution. However, we have found that the transition can be continuous or discontinuous, depending on the excitatory-inhibitory imbalance in the network. Networks with Gaussian coupling and networks with Cauchy coupling and additional additive noise lack the percolation transition in the thermodynamic limit.

cond-mat.dis-nn↗

arXiv2026

Macroscopic dynamics of quadratic integrate-and-fire neurons subject to correlated noise

The presence of correlated noise, arising from a mixture of independent fluctuations and a common noisy input shared across the neural population, is a ubiquitous feature of neural circuits, yet its impact on collective network dynamics remains poorly understood. We analyze a network of quadratic integrate-and-fire neurons driven by Gaussian noise with a tunable degree of correlation. Using the cumulant expansion method, we derive a reduced set of effective mean-field equations that accurately describe the evolution of the population's mean firing rate and membrane potential. Our analysis reveals a counterintuitive phenomenon: increasing the noise correlation strength suppresses the mean network activity, an effect we term correlated-noise-inhibited spiking. Furthermore, within a specific parameter regime, the network exhibits metastability, manifesting itself as spontaneous, noise-driven transitions between distinct high- and low-activity states. These results provide a theoretical framework for reducing the dynamics of complex stochastic networks and demonstrate how correlated noise can fundamentally regulate macroscopic neural activity, with implications for understanding state transitions in biological systems.

q-bio.NC↗

arXiv2024

Trade-off between coherence and dissipation for excitable phase oscillators

Thermodynamic uncertainty relation (TUR) bounds coherence in stochastic oscillatory systems. In this paper, we show that both dynamical and thermodynamic bounds play important roles for the excitable oscillators, e.g. neurons. Firstly, we investigate the trade-off between coherence and dissipation both in the sub and super-threshold regions for a single excitable unit, where both the TUR and the SNIC bounds constrain the fluctuation of inter-spike intervals. Secondly, we show that the widely studied phenomenon called coherence resonance, where there exists a noise strength to make the oscillatory responses of the system most coherent, is also bounded by the TUR in the one-dimensional excitable phase model. Finally, we study the coherence-dissipation relation in ensembles of strongly coupled excitable oscillators.

cond-mat.stat-mech↗

arXiv2022

Noise induced swarming of active particles

We report on the effect of spatially correlated noise on the velocities of self propelled particles. Correlations in the random forces acting on self propelled particles can induce directed collective motion, i.e. swarming. Even with repulsive coupling in the velocity directions, which favors a disordered state, strong correlations in the fluctuations can align the velocities locally leading to a macroscopic, turbulent velocity field. On the other hand, while spatially correlated noise is aligning the velocities locally, the swarming transition to globally directed motion is inhibited when the correlation length of the noise is nonzero, but smaller than the system size. We analyze the swarming transition in $d$ dimensional space in a mean field model of globally coupled velocity vectors.

cond-mat.soft↗

arXiv2021

Transition to Synchrony in a Three-Dimensional Swarming Model with Helical Trajectories

We investigate the transition from incoherence to global collective motion in a three-dimensional swarming model of agents with helical trajectories, subject to noise and global coupling. Without noise this model was recently proposed as a generalization of the Kuramoto model and it was found that alignment of the velocities occurs discontinuously for arbitrarily small attractive coupling. Adding noise to the system resolves this singular limit and leads to a continuous transition, either to a directed collective motion or to center-of-mass rotations.

cond-mat.stat-mech↗

arXiv2019

Repulsively Coupled Kuramoto-Sakaguchi Phase Oscillators Ensemble Subject to Common Noise

We consider the Kuramoto-Sakaguchi model of identical coupled phase oscillators with a common noisy forcing. While common noise always tends to synchronize the oscillators, a strong repulsive coupling prevents the fully synchronous state and leads to a nontrivial distribution of oscillator phases. In previous numerical simulations, a formation of stable multicluster states has been observed in this regime. However we argue here, that because identical phase oscillators in the Kuramoto-Sakaguchi model form a partially integrable system according to the Watanabe-Strogatz theory, the formation of clusters is impossible. Integrating with various time steps reveals that clustering is a numerical artifact, explained by the existence of higher order Fourier terms in the errors of the employed numerical integration schemes. Monitoring the induced change in certain integrals of motion we quantify these errors. We support these observations by showing, on the basis of the analysis of the corresponding Fokker-Planck equation, that two-cluster states are non-attractive. On the other hand, in ensembles of general limit cycle oscillators, such as Van der Pol oscillators, due to an anharmonic phase response function, as well as additional amplitude dynamics, multiclusters can occur naturally.

cond-mat.stat-mech↗

arXiv2019

Stochastic bursting in unidirectionally delay-coupled noisy excitable systems

We show that \emph{stochastic bursting} is observed in a ring of unidirectional delay-coupled noisy excitable systems, thanks to the combinational action of time-delayed coupling and noise. Under the approximation of timescale separation, i.e., when the time delays in each connection are much larger than the characteristic duration of the spikes, the observed rather coherent spike pattern can be described by idealized coupled point processes with a leader-follower relationship. We derive analytically the statistics of the spikes in each unit, pairwise correlations between any two units, and the spectrum of the total output from the network. Theory is in a good agreement with the simulations with a network of theta-neurons.

cond-mat.dis-nn↗

arXiv2018

Delay-induced stochastic bursting in excitable noisy systems

We show that a cumulative action of noise and delayed feedback on an excitable theta-neuron leads to rather coherent stochastic bursting. An idealized point process, valid if the characteristic time scales in the problem are well-separated, is used to describe statistical properties such as the power spectrum and the interspike interval distribution. We show how the main parameters of the point process, the spontaneous excitation rate and the probability to induce a spike during the delay action, can be calculated from the solutions of a stationary and a forced Fokker-Planck equation.

cond-mat.stat-mech↗