arXiv subjects

Jinjie Zhu

Publications and source records attributed to Jinjie Zhu.

14 recordsLinked to original sources

arXiv2026

Frequency Heterogeneity can Promote Order yet Undermine Stability in Kuramoto Networks with Higher-Order Interactions

We investigate the interplay between frequency heterogeneity and higher-order triadic interactions in a ring network of Kuramoto oscillators. While both factors individually disrupt ordered states, their combination produces unexpected collective behavior. In the strong triadic coupling regime, moderate frequency heterogeneity substantially increases the global order parameter, with an optimal heterogeneity strength growing approximately linearly with triadic coupling strength. Basin stability analysis reveals that this order-promoting effect arises from a global restructuring of the attractor landscape: frequency heterogeneity shifts the attractor competition in favor of more ordered configurations. Linear stability analysis of frequency-locked twisted states reveals a competing effect: frequency heterogeneity monotonically erodes linear stability and reduces the probability of frequency locking. These two competing mechanisms, basin enlargement and linear destabilization, together account for the non-monotonic dependence of the order parameter on heterogeneity strength. Our results demonstrate that frequency heterogeneity can play a constructive role in oscillator networks with higher-order interactions.

nlin.AO↗

arXiv2026

Optimal Fluctuations for Discrete-time Markov Jump Processes

In the last few decades, noise-induced large fluctuations and transition phenomena have garnered significant attention in a variety of scientific contexts. The concept of prehistory probability has been proposed within the framework of Langevin dynamics to illustrate the focusing effect of large fluctuation paths onto a deterministic trajectory known as the optimal path. The present paper is devoted to showing that such a focusing effect persists within the framework of discrete-time Markov jump processes. Our proof leverages large deviation theory and the concept of time reversal for Markov jump processes. A key finding is the relationship identified between the optimal path and the time reversal of a specific family of probability distributions. This theoretical framework elucidates how an essentially deterministic mechanism can emerge from rare stochastic events in discrete-time Markov jump systems.

math.PR↗

arXiv2025

Moderate Higher-Order Interactions Enhance Stability While Preserving Basin Structure

Synchronization is a ubiquitous phenomenon in complex systems. The Kuramoto model serves as a paradigmatic framework for understanding how coupled oscillators achieve collective rhythm. Conventional approaches focus on pairwise interactions, but real-world systems frequently involve higher-order couplings among multiple elements. Previous studies have shown that higher-order interactions enrich dynamics but generally shrink the attraction basin of synchronized states, making synchronization harder to achieve. Here, we demonstrate this picture is incomplete. Through systematic analysis of twisted states on ring networks, we identify a moderate coupling regime where higher-order interactions enhance stability without altering basin structure. The relative distribution among twisted states remains constant, yet quasipotential barriers deepen as coupling strengths increase. By measuring mean first passage times, we show both pairwise and higher-order couplings contribute synergistically to enhance stability, consistent with large deviation theory. These findings provide new insights into the role of higher-order interactions in synchronization.

nlin.AO↗

arXiv2025

Network stochastic resonance under higher-order interactions

Although stochastic resonance phenomena are ubiquitous across various complex systems, the influence mechanisms of higher-order interactions remain elusive. Here, we address this gap by investigating stochastic resonance in coupled phase oscillators with triadic interactions on ring networks that feature periodic modulation of the triadic coupling strength and additive noise. Our analysis reveals that higher-order interactions create fundamentally different resonance landscapes through time-varying potential wells generated by periodic modulation of triadic coupling, enabling novel noise-enhanced processing mechanisms. Additionally, weaker pairwise coupling amplifies resonance effects, while moderate network connectivity appears optimal compared to extensive connections. Our findings establish fundamental principles for network stochastic resonance and provide insights for enhanced signal processing in complex networks.

nlin.AO↗

arXiv2025

Optimal Fluctuations for Nonlinear Chemical Reaction Systems with General Rate Law

This paper investigates optimal fluctuations for chemical reaction systems with N species, M reactions, and general rate law. In the limit of large volume, large fluctuations for such models occur with overwhelming probability in the vicinity of the so-called optimal path, which is a basic consequence of the Freidlin-Wentzell theory, and is vital in biochemistry as it unveils the almost deterministic mechanism concealed behind rare noisy phenomena such as escapes from the attractive domain of a stable state and transitions between different metastable states. In this study, an alternative description for optimal fluctuations is proposed in both non-stationary and stationary settings by means of a quantity called prehistory probability in the same setting, respectively. The evolution law of each of them is derived, showing their relationship with the time reversal of a specified family of probability distributions respectively. The law of large numbers and the central limit theorem for the reversed processes are then proved. In doing so, the prehistorical approach to optimal fluctuations for Langevin dynamics is naturally generalized to the present case, thereby suggesting a strong connection between optimal fluctuations and the time reversal of the chemical reaction model.

math.PR↗

arXiv2025

How do higher-order interactions shape the energy landscape?

Understanding how higher-order interactions shape the energy landscape of coupled oscillator networks is crucial for characterizing complex synchronization phenomena. Here, we investigate a generalized Kuramoto model with triadic interactions, combining deterministic basin analysis, noise-induced transitions, and quantum annealing methods. We uncover a dual effect of higher-order interactions: they simultaneously expand basins for non-twisted states while contracting those of twisted states, yet modify potential well depths for both. As triadic coupling strengthens, higher-winding-number states and non-twisted states gain stability relative to synchronized states. The system exhibits remarkable stability asymmetry, where states with small basins can possess deep potential wells, making them highly resistant to noise-induced transitions once formed. These findings extend quasipotential theory to high-dimensional networked systems and offer new insights for controlling synchronization in complex systems.

nlin.AO↗

arXiv2024

Inverse stochastic resonance in adaptive small-world neural networks

Inverse stochastic resonance (ISR) is a phenomenon where noise reduces rather than increases the firing rate of a neuron, sometimes leading to complete quiescence. ISR was first experimentally verified with cerebellar Purkinje neurons. These experiments showed that ISR enables optimal information transfer between the input and output spike train of neurons. Subsequent studies demonstrated the efficiency of information processing and transfer in neural networks with small-world topology. We conducted a numerical investigation into the impact of adaptivity on ISR in a small-world network of noisy FitzHugh-Nagumo (FHN) neurons, operating in a bistable regime with a stable fixed point and a limit cycle -- a prerequisite for ISR. Our results show that the degree of ISR is highly dependent on the FHN model's timescale separation parameter $ε$. The network structure undergoes dynamic adaptation via mechanisms of either spike-time-dependent plasticity (STDP) with potentiation-/depression-domination parameter $P$, or homeostatic structural plasticity (HSP) with rewiring frequency $F$. We demonstrate that both STDP and HSP amplify ISR when $ε$ lies within the bistability region of FHN neurons. Specifically, at larger values of $ε$ within the bistability regime, higher rewiring frequencies $F$ enhance ISR at intermediate (weak) synaptic noise intensities, while values of $P$ consistent with depression-domination (potentiation-domination) enhance (deteriorate) ISR. Moreover, although STDP and HSP parameters may jointly enhance ISR, $P$ has a greater impact on ISR compared to $F$. Our findings inform future ISR enhancement strategies in noisy artificial neural circuits, aiming to optimize information transfer between input and output spike trains in neuromorphic systems, and prompt venues for experiments in neural networks.

nlin.AO↗

arXiv2023

Phase-Amplitude Reduction and Optimal Phase Locking of Collectively Oscillating Networks

We present a phase-amplitude reduction framework for analyzing collective oscillations in networked dynamical systems. The framework, which builds on the phase reduction method, takes into account not only the collective dynamics on the limit cycle but also deviations from it by introducing amplitude variables and using them with the phase variable. The framework allows us to study how networks react to applied inputs or coupling, including their synchronization and phase-locking, while capturing the deviations of the network states from the unperturbed dynamics. Numerical simulations are used to demonstrate the effectiveness of the framework for networks composed of FitzHugh-Nagumo elements. The resulting phase-amplitude equation can be used in deriving optimal periodic waveforms or introducing feedback control for achieving fast phase locking while stabilizing the collective oscillations.

nlin.AO↗

arXiv2023

Self-induced-stochastic-resonance breathing chimeras

The study in [Phys. Rev. Lett. 117, 014102 (2016)] discovered a novel type of chimera state known as coherence-resonance chimera (CRC), which combines the effects of coherence resonance (CR) and the spatial property of classical chimeras. In this Letter, we present yet another novel form of chimera, which we refer to as self-induced-stochastic-resonance breathing chimera (SISR-BC), which differs fundamentally from the CRC in that it combines the mechanism and effects of self-induced stochastic resonance (SISR, previously shown in [Phys. Rev. E 72, 031105 (2005)] to be intrinsically different from CR), the symmetry breaking in the rotational coupling between the slow and fast subsystems of the coupled oscillators, and the property of breathing chimera -- a form of chimera state characterized by non-stationary periodic dynamics of coherent-incoherent patterns with a periodically oscillating global order parameter. Unlike other types of chimeras, including CRC, SISR-BC demonstrates remarkable resilience to a relatively wide range of stochastic perturbations and persists even when the purely excitable system is significantly distant from the Hopf bifurcation threshold -- thanks to the mechanism of SISR -- and globally attract random distributions of initial conditions. Considering its potential impact on information processing in neuronal networks, SISR-BC could have special significance and applications.

nlin.AO↗

arXiv2022

Noise-tuned bursting in a Hedgehog burster

Noise can shape the firing behaviors of neurons. Here, we show that noise acting on the fast variable of the Hedgehog burster can tune the spike counts of bursts via the self-induced stochastic resonance (SISR) phenomenon. Using the distance matching condition, the critical transition positions on the slow manifolds can be predicted and the stochastic periodic orbits for various noise strengths are obtained. The critical transition positions on the slow manifold with non-monotonic potential differences exhibit a staircase-like dependence on the noise strength, which is also revealed by the stepwise change in the period of the stochastic periodic orbit. The noise-tuned bursting is more coherent within each step while displaying mixed-mode oscillations near the boundaries between the steps. When noise is large enough, noise-induced trapping of the slow variable can be observed, where the number of coexisting traps increases with the noise strength. It is argued that the robustness of SISR underlies the generality of the results discovered in this paper.

nlin.AO↗

arXiv2022

Phase dynamics of noise-induced coherent oscillations in excitable systems

Noise can induce coherent oscillations in excitable systems without periodic orbits. Here, we establish a method to derive a hybrid system approximating the noise-induced coherent oscillations in excitable systems and further perform phase reduction of the hybrid system to derive an effective, dimensionality-reduced phase equation. We apply the reduced phase model to a periodically forced excitable system and two-coupled excitable systems, both undergoing noise-induced oscillations. The reduced phase model can quantitatively predict the entrainment of a single system to the periodic force and the mutual synchronization of two coupled systems, including the phase slipping behavior due to noise, as verified by Monte Carlo simulations. The derived phase model gives a simple and efficient description of noise-induced oscillations and can be applied to the analysis of more general cases.

nlin.AO↗

arXiv2021

Asymptotic phase and amplitude for classical and semiclassical stochastic oscillators via Koopman operator theory

The asymptotic phase is a fundamental quantity for the analysis of deterministic limit-cycle oscillators, and generalized definitions of the asymptotic phase for stochastic oscillators have also been proposed. In this article, we show that the asymptotic phase and also amplitude can be defined for classical and semiclassical stochastic oscillators in a natural and unified manner by using the eigenfunctions of the Koopman operator of the system. We show that the proposed definition gives appropriate values of the phase and amplitude for strongly stochastic limit-cycle oscillators, excitable systems undergoing noise-induced oscillations, and also for quantum limit-cycle oscillators in the semiclassical regime.

nlin.CD↗

arXiv2021

Stochastic periodic orbits in fast-slow systems with self-induced stochastic resonance

Noise is ubiquitous in various systems. In systems with multiple timescales, noise can induce various coherent behaviors. Self-induced stochastic resonance (SISR) is a typical noise-induced phenomenon identified in such systems, wherein noise acting on the fast subsystem causes stochastic resonancelike boundary crossings. In this paper, we analyze the stochastic periodic orbits caused by SISR in fast-slow systems. By introducing the notion of the mean first passage velocity toward the boundary, a distance matching condition is established, through which the critical transition position of boundary crossing can be calculated. The theoretical stochastic periodic orbit can be accordingly obtained via gluing the dynamics along the slow manifolds. It is shown that the theoretical predictions are in excellent agreement with the results of Monte Carlo simulations for a piecewise linear FitzHugh-Nagumo system even for large noise. Furthermore, the proposed method is extended to the original FitzHugh-Nagumo system and also found to exhibit consistent accuracy. These results provide insights into the mechanisms of coherent behaviors in fast-slow systems and will shed light on the coherent behaviors in more complex systems and large networks.

nlin.AO↗

arXiv2021

Spatial phase sensitivity for oscillators close to the saddle-node homoclinic bifurcation

The traditional phase sensitivity function (PSF) has manifested its efficacy in investigating synchronization behaviors for limit-cycle oscillators. However, some subtle details may be ignored when the phase value is accumulated in space or the perturbation is space-dependent. In this paper, we compared spatial PSF with the traditional PSF for oscillators close to the saddle-node homoclinic (SNH) bifurcation, also known as saddle-node on invariant circle (SNIC) bifurcation. It is found that the spatial phase sensitivity function could reveal the phase accumulation feature on the limit cycle. Moreover, it is proved that for any two-dimensional smooth dynamical system, type II phase response curve is the only possible type. Finally, the synchronization distributions of uncoupled SNH oscillator driven by common and independent noises are studied, which shows the space-dependent coupling function of common noise could have significant influences on the synchronization behavior.

nlin.AO↗