相关论文: Instabilities in associative memory model with syn…
Dynamical mean-field theory is used to study the magnetic instabilities and phase diagram of the double-exchange (DE) model with Hund's coupling J_H >0 in infinite dimensions. In addition to ferromagnetic (FM) and antiferromagnetic (AF)…
We study binary state contagion dynamics on a social network where nodes act in response to the average state of their neighborhood. We model the competing tendencies of imitation and non-conformity by incorporating an off-threshold into…
We study the evolution of linear density perturbations in the context of interacting scalar field-dark matter cosmologies, where the presence of the coupling acts as a stabilization mechanism for the runaway behavior of the scalar…
Thermoacoustic instabilities observed in turbulent combustion systems have disastrous consequences and are notoriously challenging to model, predict and control. Here, we introduce a mean-field model of thermoacoustic transitions, where the…
In this paper we introduce a class of stochastic population models based on "patch dynamics". The size of the patch may be varied, and this allows one to quantify the departures of these stochastic models from various mean field theories,…
Non-equilibrium dynamics are present in many aspects of our lives, ranging from microscopic physical systems to the functioning of the brain. What characterizes stochastic models of non-equilibrium processes is the breaking of the…
In this paper, the problem of non-fragile finite-time stabilization for linear discrete mean-field stochastic systems is studied. The uncertain characteristics in control parameters are assumed to be random satisfying the Bernoulli…
Emotional disorders and psychological flourishing are the result of complex interactions between positive and negative affects that depend on external events and the subject's internal representations. Based on psychological data, we…
We consider a neural network with adapting synapses whose dynamics can be analitically computed. The model is made of $N$ neurons and each of them is connected to $K$ input neurons chosen at random in the network. The synapses are…
We present a unified field-theoretic framework for the dynamics of activity and connectivity in interacting neuronal systems. Building upon previous works, where a field approach to activity--connectivity dynamics, formation of collective…
Impulsive systems are a very flexible class of systems that can be used to represent switched and sampled-data systems. We propose to extend here the previously obtained results on deterministic impulsive systems to the stochastic setting.…
In this paper, we characterize major depression (MD) as a complex dynamical system in which symptoms (e.g., insomnia and fatigue) are directly connected to one another in a network structure. We hypothesize that individuals can be…
We study the impact of noise on a neural population rate model of up and down states. Up and down states are typically observed in neuronal networks as a slow oscillation, where the population switches between high and low firing rates…
Dynamic functional connectivity (DFC) analysis involves measuring correlated neural activity over time across multiple brain regions. Significant regional correlations among neural signals, such as those obtained from resting-state…
We present a stochastic differential equation model of suicidal progression in U.S. veterans, simulating transitions across mental health states under dynamic stress and covariate influence. Transition rates are modulated by an…
Stochastic reaction networks are mathematical models frequently used in, but not limited to, biochemistry. These models are continuous-time Markov chains whose transition rates depend on certain parameters called rate constants, which…
We use a mean-field-based transformer model to theoretically investigate how auxiliary variables, such as positional encoding, prevent mode collapse of self-attention mechanisms. The use of mean-field transformers to analyze the properties…
We study extremely diluted spin models of neural networks in which the connectivity evolves in time, although adiabatically slowly compared to the neurons, according to stochastic equations which on average aim to reduce frustration. The…
Nonequilibrium behavior and dynamic phase transition properties of a kinetic Ising model under the influence of periodically oscillating random-fields have been analyzed within the framework of effective field theory (EFT) based on a…
A two-dimensional small-world type network, subject to spatial prisoners' dilemma dynamics and containing an influential node defined as a special node with a finite density of directed random links to the other nodes in the network, is…