Related papers: Complete mathematical characterization of two simp…
This paper presents a stability analysis of simple neuromodules displaying fold bifurcations (leading to hysteresis), flip bifurcations (period doubling and undoubling to and from chaos) and Neimark-Sacker bifurcations (quasiperiodic and…
Ordinary differential equations (ODEs) can model the transition of cell states over time. Bifurcation theory is a branch of dynamical systems which studies changes in the behavior of an ODE system while one or more parameters are varied. We…
Many dynamical systems arising in biology and other areas exhibit multistationarity (two or more positive steady states with the same conserved quantities). Although deciding multistationarity for a polynomial dynamical system is an…
This paper presents an algorithm for approximating certain types of dynamical systems given by a system of ordinary delay differential equations by a Boolean network model. Often Boolean models are much simpler to understand than complex…
Traveling wavetrains in generalized two-species predator-prey models and two-component reaction-diffusion equations are considered. The stability of the fixed points of the traveling wave ODEs (in the usual "spatial" variable) is…
In this paper, we study the classical two-predators-one-prey model. The classical model described by a system of 3 ordinary differential equations can be reduced to a one-dimensional bimodal map. We prove that this map has at most two…
Stochastic resonance is a well established phenomenon, which proves relevant for a wide range of applications, of broad trans-disciplinary breath. Consider a one dimensional bistable stochastic system, characterized by a deterministic…
The neural dynamics of the nematode C. elegans are experimentally low-dimensional and correspond to discrete behavioral states, where previous modeling work has found neural proxies for some of these states. Experimental results further…
Complex dynamical systems are often modeled as networks, with nodes representing dynamical units which interact through the network's links. Gene regulatory networks, responsible for the production of proteins inside a cell, are an example…
Stochastic oscillations in individual cells are usually characterized by a non-monotonic power spectrum with an oscillatory autocorrelation function. Here we develop an analytical approach of stochastic oscillations in a minimal hybrid…
In this paper, we study the stability of an Ordinary Differential Equation (ODE) usually referred to as Cyclic Feedback Loop, which typically models a biological network of molecules where each molecule regulates its successor in a cycle.…
A dynamic logic method was developed to analyze molecular networks of cells by combining Kauffman and Thomas's logic operations with molecular interaction parameters. The logic operations characterize the discrete interactions between…
We consider a porous media equation with balanced bistable reactions, equipped with some general nonlinear boundary condition. When the coefficient of the reaction term is much larger than that of the diffusion term, we see that, besides…
Diverse biological networks exhibit universal features distinguished from those of random networks, calling much attention to their origins and implications. Here we propose a minimal evolution model of Boolean regulatory networks, which…
Motile eukaryotic cells display distinct modes of migration that often occur within the same cell type. It remains unclear, however, whether transitions between the migratory modes require changes in external conditions, or whether the…
We review some properties of dynamical systems with slowly varying parameters, when a parameter is moved through a bifurcation point of the static system. Bifurcations with a single zero eigenvalue may create hysteresis cycles, whose area…
Key features of biological activity can often be captured by transitions between a finite number of semi-stable states that correspond to behaviors or decisions. We present here a broad class of dynamical systems that are ideal for modeling…
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…
In this paper we describe the solution of a stochastic bistable system from a dynamical perspective. We show how a single framework with variable noise can explain hysteresis at zero temperature and two-state coexistence in the presence of…
Considerable evidence suggests that anticipating sudden shifts from one state to another in bistable dynamical systems is a challenging task, examples include ecosystems, financial markets, complex diseases, etc. In this paper, we…