Related papers: Widespread quasi-steady state assumption in biolog…
The appearance of so-called exceptional points in the complex spectra of non-Hermitian systems is often associated with phenomena that contradict our physical intuition. One example of particular interest is the state-exchange process…
There are many mathematical models of biochemical cell signaling pathways that contain a large number of elements (species and reactions). This is sometimes a big issue for identifying critical model elements and describing the model…
Systems with long-range interactions, while relaxing towards equilibrium, sometimes get trapped in long-lived non-Boltzmann quasistationary states (QSS) which have lifetimes that grow algebraically with the system size. Such states have…
For a large class of processes with an absorbing state, statistical properties of the surviving sample attain time-independent values in the quasi-stationary (QS) regime. We propose a practical simulation method for studying…
Living systems, from single cells to higher vertebrates, receive a continuous stream of non-stationary inputs that they sense, e.g., via cell surface receptors or sensory organs. Integrating these time-varying, multi-sensory, and often…
Noise plays a fundamental role in a wide variety of physical and biological dynamical systems. It can arise from an external forcing or due to random dynamics internal to the system. It is well established that even weak noise can result in…
Transitions between nonequilibrium steady states obey a generalized Clausius inequality, which becomes an equality in the quasistatic limit. For slow but finite transitions, we show that the behavior of the system is described by a response…
Consider a mathematical model of evolutionary adaptation of fitness landscape and mutation matrix as a reaction to population changes. As a basis, we use an open quasispecies model, which is modified to include explicit death flow. We…
We analyst in detail a new approach to the monitoring and forecasting of the onset of transitions in high dimensional complex systems (see Phys. Rev. Lett . vol. 113, 264102 (2014)) by application to the Tangled Nature Model of evolutionary…
Coherent oscillatory activity can arise spontaneously as a result of increased coupling in a system of excitable and passive cells, each being quiescent in isolation. This can potentially explain the appearance of spontaneous rhythmic…
The quasi-steady-state approximation (or stochastic averaging principle) is a useful tool in the study of multiscale stochastic systems, giving a practical method by which to reduce the number of degrees of freedom in a model. The method is…
We study dynamical phase transitions in systems with long-range interactions, using the Hamiltonian Mean Field (HMF) model as a simple example. These systems generically undergo a violent relaxation to a quasi-stationary state (QSS) before…
Mathematical analysis of mass action models of large complex chemical systems is typically only possible if the models are reduced. The most common reduction technique is based on quasi-steady state assumptions. To increase the accuracy of…
For a model long-range interacting system of classical Heisenberg spins, we study how fluctuations, such as those arising from having a finite system size or through interaction with the environment, affect the dynamical process of…
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…
The quasi steady-state (QSS) model tries to reach a good compromise between accuracy and efficiency in long-term stability analysis. However, the QSS model is unable to provide correct approximations and stability assessment for the…
We develop a quasilinear theory of the Vlasov equation in order to describe the approach of systems with long-range interactions to quasi-stationary states. We derive a diffusion equation governing the evolution of the velocity distribution…
Stochastic dynamics of chemical reactions in a mutually repressing two-gene circuit is numerically simulated. The circuit has a rich variety of different states when the kinetic change of DNA status is slow. The stochastic switching…
The fidelity of operations on a solid-state quantum processor is fundamentally bounded by environmental decoherence. Characterizing environmental fluctuations is challenging because the acquisition time of nonadaptive experimental protocols…
The quasi-steady-state assumption (QSSA) is an approximation that is widely used in chemistry and chemical engineering to simplify reaction mechanisms. The key step in the method requires a solution by radicals of a system of multivariate…