Related papers: Singularly Perturbed Monotone Systems and an Appli…

Interacting particle systems are continuous time Markov processes which are used to construct models in many disciplines. Monotonicity is a property that some interacting particle systems possess. A monotone interacting particle system is…

Living systems adapt to various environmental conditions by changing their internal states. Inspired by gene expression and epigenetic modification dynamics, we herein propose a generic mechanism for adaptation by combining fast oscillatory…

The dynamics of a linear dynamical system over a finite field can be described by using the elementary divisors of the corresponding matrix. It is natural to extend the investigation to a general finite commutative ring. In a previous…

In this paper, we investigate a class of port-Hamiltonian systems with singular vector fields. We show that, under suitable conditions, their interconnection with passive systems ensures convergence to a prescribed non-equilibrium steady…

We investigate the weak-strong coupling transition of two linearly coupled systems under the influence of a phase fluctuating coupling. In the weak coupling regime the exponential decay of quantum properties is well known. A different…

We present a simple two-dimensional dynamical system where two nonlinear terms, exerting respectively positive feedback and reversal, compete to create a singularity in finite time decorated by accelerating oscillations. The power law…

In adaptive dynamical networks, the dynamics of the nodes and the edges influence each other. We show that we can treat such systems as a closed feedback loop between edge and node dynamics. Using recent advances on the stability of…

Oscillations play a major role in a number of biological systems, from predator-prey models of ecology to circadian clocks. In this paper we focus on the question of whether oscillations exist within dual-site phosphorylation systems.…

Habituation - a phenomenon in which a dynamical system exhibits a diminishing response to repeated stimulations that eventually recovers when the stimulus is withheld - is universally observed in living systems from animals to unicellular…

Transversality of stable and unstable manifolds of hyperbolic periodic trajectories is proved for monotone cyclic systems with negative feedback. Such systems in general are not in the category of monotone dynamical systems in the sense of…

The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable…

We present initial results regarding the existence, stability and interaction of linear and nonlinear vibrational modes in a system of two coupled, one dimensional lattices with unequal numbers of masses. The effects on these nonlinear…

"Synchronization of two dynamical systems" is the term used to describe the phenomenon when two or more systems gradually change their states or behaviors to become similar or identical. This can happen in a lot of fields, such as physics,…

Dual phospho/dephosphorylation cycles, as well as covalent enzymatic-catalyzed modifications of substrates, are widely diffused within cellular systems and are crucial for the control of complex responses such as learning, memory and…

In this work, it is demonstrated that the usual power system dynamic model exhibits a feedforward-feedback control structure. The distinct properties of the feedforward and feedback subsystems are identified and studied using respective…

Background: Using a statistical physics approach, we study the stochastic switching behavior of a model circuit of multisite phosphorylation and dephosphorylation with feedback. The circuit consists of a kinase and phosphatase acting on…

Multistationarity in biological systems is a mechanism of cellular decision making. In particular, signaling pathways regulated by protein phosphorylation display features that facilitate a variety of responses to different biological…

Multistationarity in molecular systems underlies switch-like responses in cellular decision making. Determining whether and when a system displays multistationarity is in general a difficult problem. In this work we completely determine the…

We study in this paper certain properties of the responses of dynamical systems to external inputs. The motivation arises from molecular systems biology. and, in particular, the recent discovery of an important transient property, related…

This article illustrates the application of multiple scales analysis to two archetypal quasilinear systems; i.e. to systems involving fast dynamical modes, called fluctuations, that are not directly influenced by fluctuation--fluctuation…