arXiv subjects

Shenquan Liu

Publications and source records attributed to Shenquan Liu.

6 recordsLinked to original sources

arXiv2026

Dissecting emerging slow rhythms in delay-coupled neural oscillators

Synaptic transmission delays are ubiquitous in neural circuits and can alter the dynamical repertoire of coupled oscillators quantitatively and qualitatively. Here, we demonstrate that delayed coupling in inhibitory networks introduces an effective slow-fast structure in the phase-difference dynamics, generating low-frequency components that are not due to intrinsic cellular properties, and we show that this behavior is not specific to a particular model structure. The origin of this generic phenomenon is analyzed by numerical continuation and bifurcation analysis, which provides a systematic approach to find such delay-induced slow modulating rhythms. We employ phase reduction based on phase response curves to derive a phase-difference model with delay for mutually inhibitory coupled oscillators, where the individual units are given by the FitzHugh-Nagumo model, the Morris-Lecar model, or a next-generation neural mass model derived from quadratic integrate-and-fire neurons. We use phase planes to study multistability and limit cycles, which correspond to slow modulation of fast oscillations in the full model. Treating the synaptic delay as a bifurcation parameter, we apply numerical continuation to construct delay-dependent bifurcation diagrams. The analysis reveals Hopf, heteroclinic, and saddle-node-of-periodics bifurcations that cause and organize slow rhythmic behavior. Our analysis provides a systematic approach to the search for limit cycles in phase-reduction models corresponding to delay-induced slow rhythms in the original model.

nlin.CD↗

arXiv2025

Renormalization group analysis of noisy neural field

Neurons in the brain show great diversity in their individual properties and their connections to other neurons. To develop an understanding of how neuronal diversity contributes to brain dynamics and function at large scales we start with a linearized version of the Wilson-Kowan model and introduce a random anisotropy to inter-neuron connection. The resultant model is Edwards-Wilkinson model with a random anisotropic term. Averaging over the quenched randomness with the replica method we obtain a bi-quadratic nonlinearity. We use Wilsonian dynamic renormalization group to analyze this model. We find that, up to one loop order, for dimensions higher than two, the effect of the noise is to change dynamic exponent from two to one.

cond-mat.dis-nn↗

arXiv2024

Subsystem Resetting of a Heterogeneous Network of Theta Neurons

Stochastic resetting has shown promise in enhancing the stability of dynamical systems. Here, we apply this concept to theta neuron networks with partial resetting, where only a fraction of neurons is intermittently reset. We examine both infinite and finite reset rates, using the averaged firing rate as an indicator of network stability. At infinite reset rates, a high proportion of resetting neurons drives the network to stable rest or spiking states, collapsing the bistable region at the Cusp bifurcation and producing smooth transitions. Finite resetting introduces stochastic fluctuations, leading to complex dynamics that sometimes deviate from theoretical predictions. These insights highlight the role of partial resetting in stabilizing neural dynamics, with applications in biological systems and neuromorphic computing.

math.DS↗

arXiv2023

Structural constraints on the emergence of oscillations in multi-population neural networks

Oscillations arise in many real-world systems and are associated with both functional and dysfunctional states. Whether a network can oscillate can be estimated if we know the strength of interaction between nodes. But in real-world networks (in particular in biological networks) it is usually not possible to know the exact connection weights. Therefore, it is important to determine the structural properties of a network necessary to generate oscillations. Here, we provide a proof that uses dynamical system theory to prove that an odd number of inhibitory nodes and strong enough connections are necessary to generate oscillations in a single cycle threshold-linear network. We illustrate these analytical results in a biologically plausible network with either firing-rate based or spiking neurons. Our work provides structural properties necessary to generate oscillations in a network. We use this knowledge to reconcile recent experimental findings about oscillations in basal ganglia with classical findings.

q-bio.NC↗

arXiv2023

Computational model advance deep brain stimulation for Parkinson's disease

Deep brain stimulation(DBS)has become an effective intervention for advanced Parkinson's disease, but the exact mechanism of DBS is still unclear. In this review, we discuss the history of DBS, the anatomy and internal architecture of the basal ganglia(BG), the abnormal pathological changes of the BG in Parkinson's disease, and how computational models can help understand and advance DBS. We also describe two types of models:mathematical theoretical models and clinical predictive models. Mathematical theoretical models simulate neurons or neural networks of BG to shed light on the mechanistic principle underlying DBS, while clinical predictive models focus more on patients' outcomes, helping to adapt treatment plans for each patient and advance novel electrode designs. Finally, we provide insights and an outlook on future technologies.

q-bio.NC↗

arXiv2021

Episodic memory governs choices: An RNN-based reinforcement learning model for decision-making task

Typical methods to study cognitive function are to record the electrical activities of animal neurons during the training of animals performing behavioral tasks. A key problem is that they fail to record all the relevant neurons in the animal brain. To alleviate this problem, we develop an RNN-based Actor-Critic framework, which is trained through reinforcement learning (RL) to solve two tasks analogous to the monkeys' decision-making tasks. The trained model is capable of reproducing some features of neural activities recorded from animal brain, or some behavior properties exhibited in animal experiments, suggesting that it can serve as a computational platform to explore other cognitive functions. Furthermore, we conduct behavioral experiments on our framework, trying to explore an open question in neuroscience: which episodic memory in the hippocampus should be selected to ultimately govern future decisions. We find that the retrieval of salient events sampled from episodic memories can effectively shorten deliberation time than common events in the decision-making process. The results indicate that salient events stored in the hippocampus could be prioritized to propagate reward information, and thus allow decision-makers to learn a strategy faster.

q-bio.NC↗