Related papers: Nonlinear signal transduction network with multist…
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…
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…
Neuronal networks alternate between high- and low-activity regimes, known as up and down states. They also display rhythmic patterns essential for perception, memory consolidation, and sensory processing. Despite their importance, the…
Nonlinear systems driven by recurrent signals are known to exhibit complex dynamical responses which, in the physiological context, can have important functional consequences. One of the simplest biological systems that is exposed to such…
The critical boundaries separating ordered from chaotic behavior in randomly wired S-state networks are calculated. These networks are a natural generalization of random Boolean nets and are proposed as on extended approach to genetic…
Statistical properties of environments experienced by biological signaling systems in the real world change, which necessitate adaptive responses to achieve high fidelity information transmission. One form of such adaptive response is gain…
Many natural systems are organized as networks, in which the nodes (be they cells, individuals or populations) interact in a time-dependent fashion. The dynamic behavior of these networks depends on how these nodes are connected, which can…
We consider a general model in which there is a coupled dynamics of node states and links states in a network. This coupled dynamics coevolves with dynamical changes of the topology of the network caused by a link rewiring mechanism. Such…
Random walks represent an important tool for probing the structural and dynamical properties of networks and modeling transport and diffusion processes on networks. However, when individuals' movement becomes dictated by more complicated…
We study the evolution of a random weighted network with complex nonlinear dynamics at each node, whose activity may cease as a result of interactions with other nodes. Starting from a knowledge of the micro-level behaviour at each node, we…
Perturbations are ubiquitous in metabolism. A central tool to understand and control their influence on metabolic networks is sensitivity analysis, which investigates how the network responds to external perturbations. We follow here a…
External flows of energy, entropy, and matter can cause sudden transitions in the stability of biological and industrial systems, fundamentally altering their dynamical function. How might we control and design these transitions in chemical…
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…
Despite their topological complexity almost all functional properties of metabolic networks can be derived from steady-state dynamics. Indeed, many theoretical investigations (like flux-balance analysis) rely on extracting function from…
Switch-like responses arising from bistability have been linked to cell signaling processes and memory. Revealing the shape and properties of the set of parameters that lead to bistability is necessary to understand the underlying…
Simple nonlinear dynamical systems with multiple stable stationary states are often taken as models for switchlike biological systems. This paper considers the interaction of multiple such simple multistable systems when they are embedded…
We study a non-linear dynamical system on networks inspired by the pitchfork bifurcation normal form. The system has several interesting interpretations: as an interconnection of several pitchfork systems, a gradient dynamical system and…
Linearized catalytic reaction equations modeling e.g. the dynamics of genetic regulatory networks under the constraint that expression levels, i.e. molecular concentrations of nucleic material are positive, exhibit nontrivial dynamical…
Athermal models of disordered fibrous networks are highly useful for studying the mechanics of elastic networks composed of stiff biopolymers. The underlying network architecture is a key aspect that can affect the elastic properties of…
Single trial analyses of ensemble activity in alert animals demonstrate that cortical circuits dynamics evolve through temporal sequences of metastable states. Metastability has been studied for its potential role in sensory coding, memory…