Related papers: Switching in mass action networks based on linear …
This paper deals a continuous-time state-dependent jump linear system, a particular kind of stochastic switching system. In particular, we consider a situation when the transition rate of the random jump process depends on the state…
This paper deals with stability of discrete-time switched linear systems whose all subsystems are unstable and the set of admissible switching signals obeys pre-specified restrictions on switches between the subsystems and dwell times on…
This paper presents a stability test for a class of interconnected nonlinear systems motivated by biochemical reaction networks. One of the main results determines global asymptotic stability of the network from the diagonal stability of a…
A fundamental premise of statistical physics is that the particles in a physical system are interchangeable, and hence the state of each specific component is representative of the system as a whole. This assumption breaks down for complex…
In Systems Biology there is a growing interest in the question, whether or not a given mathematical model can admit more than one steady state. As parameter values are often unknown or subject to a very high uncertainty, one is often…
In an adaptive population which models financial markets and distributed control, we consider how the dynamics depends on the diversity of the agents' initial preferences of strategies. When the diversity decreases, more agents tend to…
In many non-linear systems, such as plasma oscillation, boson condensation, chemical reaction, and even predatory-prey oscillation, the coarse-grained dynamics are governed by an equation containing anti-symmetric transitions, known as the…
This paper deals with stability of discrete-time switched linear systems whose all subsystems are unstable. We present sufficient conditions on the subsystems matrices such that a switched system is globally exponentially stable under a set…
Stochastic chemical processes are described by the chemical master equation satisfying the law of mass-action. We first ask whether the dual master equation, which has the same steady state as the chemical master equation, but with inverted…
Living cells need a constant availability of certain resources to have a sustained gene expression process. Limited availability of cellular resources for gene expression, like ribosomes, along with a variation of resource affinity,…
The dynamics of network formation are generally very complex, making the study of distributions over the space of networks often intractable. Under a condition called conservativeness, I show that the stationary distribution of a network…
The goal of this paper is to understand if the property of adaptation, which is a typical property of many biochemical systems, can be achieved only by biological systems that actively consume energy or if it can be achieved also by passive…
We address the level of complexity that can be observed in the dynamics near a robust heteroclinic network. We show that infinite switching, which is a path towards chaos, does not exist near a heteroclinic network such that the eigenvalues…
The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from…
We consider exchangeable Markov multi-state survival processes -- temporal processes taking values over a state-space$\mathcal{S}$ with at least one absorbing failure state $\flat \in \mathcal{S}$ that satisfy natural invariance properties…
The nonequilibrium stationary state of an exclusive genetic switch is considered. The model comprises two competing species and a single binding site which, when bound to by a protein of one species, causes the other species to be…
Self-organized bistability (SOB) stands as a critical behavior for the systems delicately adjusting themselves to the brink of bistability, characterized by a first-order transition. Its essence lies in the inherent ability of the system to…
We consider flat differential control systems for which there exist flat outputs that are part of the state variables and study them using Jacobi bound. We introduce a notion of saddle Jacobi bound for an ordinary differential system of $n$…
Systems switching between different dynamical phases is an ubiquitous phenomenon. The general understanding of such a process is limited. To this end, we present a general expression that captures fluctuations of a system exhibiting a…
A dynamical network, a graph whose nodes are dynamical systems, is usually characterized by a large dimensional space which is not always accesible due to the impossibility of measuring all the variables spanning the state space. Therefore,…