相关论文: Amplified steady state bifurcations in feedforward…

We explore the bifurcation structure of a modified Cahn-Hilliard equation that describes a system that may undergo a first order phase transition and is kept permanently out of equilibrium by a lateral driving. This forms a simple model,…

A stochastic reaction-diffusion model is studied on a networked support. In each patch of the network two species are assumed to interact following a non-normal reaction scheme. When the interaction unit is replicated on a directed linear…

A snap-through bifurcation occurs when a bistable structure loses one of its stable states and moves rapidly to the remaining state. For example, a buckled arch with symmetrically clamped ends can snap between an inverted and a natural…

The global dynamics of gene regulatory networks are known to show robustness to perturbations in the form of intrinsic and extrinsic noise, as well as mutations of individual genes. One molecular mechanism underlying this robustness has…

The degree distribution is a key statistical indicator in network theory, often used to understand how information spreads across connected nodes. In this paper, we focus on non-growing networks formed through a rewiring algorithm and…

We demonstrate the effects of embedding subgraphs using a Boolean network, which is one of the discrete dynamical models for transcriptional regulatory networks. After comparing the dynamical properties of network embedded seven different…

Markov branching systems form a fundamental class of stochastic models that are extensively applied in biology, physics, finance, and other domains. These systems are distinguished by their continuous-time evolution and inherent branching…

Sparse random networks contain structures that can be considered as diluted feed-forward networks. Modeling of cortical circuits has shown that feed-forward structures, if strongly pronounced compared to the embedding random network, enable…

In living cells, chemical reactions form a complex network. Complicated dynamics arising from such networks are the origins of biological functions. We propose a novel mathematical method to analyze bifurcation behaviors of a reaction…

The regulation of the cell state is a complex process involving several components. These complex dynamics can be modeled using Boolean networks, allowing us to explain the existence of different cell states and the transition between them.…

Cell lineage statistics is a powerful tool for inferring cellular parameters, such as division rate, death rate or the population growth rate. Yet, in practice such an analysis suffers from a basic problem: how should we treat incomplete…

Reaction-diffusion systems with time-delay defined on complex networks have been studied in the framework of the emergence of Turing instabilities. The use of the Lambert W-function allowed us get explicit analytic conditions for the onset…

Advanced AI reasoning systems route tasks through dynamic execution graphs of specialized agents. We identify a structural blind spot in this architecture: schedulers optimize load and fitness but lack a model of how failure propagates…

Existing models of network growth typically have one or two parameters or strategies which are fixed for all times. We introduce a general framework where feedback on the current state of a network is used to dynamically alter the values of…

Building on the first part of this paper, we develop the theory of functional asynchronous networks. We show that a large class of functional asynchronous networks can be (uniquely) represented as feedforward networks connecting events or…

Directed cycles form the fundamental motifs in natural, social and artificial networks, yet their distinct computational roles remain under-explored, particularly in the context of higher-order structure and function. In this work, we…

We study the stationary states of networks consisting of weakly coupled bistable units. We prove the existence of a high multiplicity of stable steady states in networks with very general inter-unit dynamics. We present a method for…

Systems of dynamical interactions between competing species can be used to model many complex systems, and can be mathematically described by {\em random} networks. Understanding how patterns of activity arise in such systems is important…

The theory of mixed-feedback systems provides an effective framework for the design of robust and tunable oscillations in nonlinear systems characterized by interleaved fast positive and slow negative feedback loops. The goal of this paper…

Traveling fronts and stationary localized patterns in bistable reaction-diffusion systems have been broadly studied for classical continuous media and regular lattices. Analogs of such non-equilibrium patterns are also possible in networks.…