Related papers: Boolean Models of Bistable Biological Systems
Boolean networks are discrete dynamical systems where each automaton has its own Boolean function for computing its state according to the configuration of the network. The updating mode then determines how the configuration of the network…
Self-excited systems arise in many applications, such as biochemical systems, mechanical systems with fluid-structure interaction, and fuel-driven systems with combustion dynamics. This paper presents a Lur'e model that exhibits biased…
A general scheme for construction of dynamical systems able to learn generation of the desired kinds of dynamics through adjustment of their internal structure is proposed. The scheme involves intrinsic time-delayed feedback to steer the…
A network of noisy bistable elements with global time-delayed couplings is considered. A dichotomous mean field model has recently been developed describing the collective dynamics in such systems with uniform time delays near the…
Transcriptional delay can significantly impact the dynamics of gene networks. Here we examine how such delay affects bistable systems. We investigate several stochastic models of bistable gene networks and find that increasing delay…
Living systems are often described utilizing informational analogies. An important open question is whether information is merely a useful conceptual metaphor, or intrinsic to the operation of biological systems. To address this question,…
Equation learning methods present a promising tool to aid scientists in the modeling process for biological data. Previous equation learning studies have demonstrated that these methods can infer models from rich datasets, however, the…
This paper considers $L_2$ and BIBO stability and stabilization issues for systems with time-varying delays which can be of retarded or neutral type. An important role is played by a nominal system with fixed delays which are close to the…
We consider the dynamics of a population of organisms containing two mutually inhibitory gene regulatory networks, that can result in a bistable switch-like behaviour. We completely characterize their local and global dynamics in the…
Bayesian networks are a versatile and powerful tool to model complex phenomena and the interplay of their components in a probabilistically principled way. Moving beyond the comparatively simple case of completely observed, static data,…
Biological systems operate under persistent noise, which can alter system states and induce transitions between attractors. Here, we study the attractor dynamics of Boolean networks focusing on the transitions between attractors induced by…
Discrete models have a long tradition in engineering, including finite state machines, Boolean networks, Petri nets, and agent-based models. Of particular importance is the question of how the model structure constrains its dynamics. This…
We consider the rates of noise-induced switching between the stable states of dissipative dynamical systems with delay and also the rates of noise-induced extinction, where such systems model population dynamics. We study a class of systems…
Dynamic processes of interacting units on a network are out of equilibrium in general. In the case of a directed tree, the dynamic cavity method provides an efficient tool that characterises the dynamic trajectory of the process for the…
Computational models of biological processes provide one of the most powerful methods for a detailed analysis of the mechanisms that drive the behavior of complex systems. Logic-based modeling has enhanced our understanding and…
Modeling the dynamics of biological networks introduces many challenges, among them the lack of first principle models, the size of the networks, and difficulties with parameterization. Discrete time Boolean networks and related continuous…
Transcription and translation retrieve and operationalize gene encoded information in cells. These processes are not instantaneous and incur significant delays. In this paper we study Goodwin models of both inducible and repressible operons…
In this paper, we obtain sufficient conditions for the permanence of a family of nonautonomous systems of delay differential equations. This family includes structured models from mathematical biology, with either discrete or distributed…
Analysis of mathematical models in ecology and epidemiology often focuses on asymptotic dynamics, such as stable equilibria and periodic orbits. However, many systems exhibit long transient behaviors where certain aspects of the dynamics…
Bistable biological regulatory systems need to cope with stochastic noise to fine-tune their function close to bifurcation points. Here, we study stability properties of this regime in generic systems to demonstrate that cooperative…