Related papers: Bifurcation of Transition Paths Induced by Coupled…
Bifurcation analysis collects techniques for characterizing the dependence of certain classes of solutions of a dynamical system on variations in problem parameters. Common solution classes of interest include equilibria and periodic…
In this paper we consider piecewise affine differential equations modeling gene networks. We work with arbitrary decay rates, and under a local hypothesis expressed as an alignment condition of successive focal points. The interaction graph…
We consider noise-driven exit from a domain of attraction in a two-dimensional bistable system lacking detailed balance. Through analog and digital stochastic simulations, we find a theoretically predicted bifurcation of the most probable…
We consider the effect on tipping from an additive periodic forcing in a canonical model with a saddle node bifurcation and a slowly varying bifurcation parameter. Here tipping refers to the dramatic change in dynamical behavior…
Transcriptional delay can significantly impact the dynamics of gene networks. Here we examine how such delay affects bistable systems. We investigate several stochastic models of bistable gene networks and find that increasing delay…
We examine examples of weakly nonlinear systems whose steady states undergo a bifurcation with increasing forcing, such that a forced subsystem abruptly ceases to absorb additional energy, instead diverting it into an initially quiescent,…
Oscillatory systems with time-delayed pulsatile feedback appear in various applied and theoretical research areas, and received a growing interest in the last years. For such systems, we report a remarkable scenario of destabilization of a…
We analyze rate-dependent tipping in a fast/slow system with an equilibrium near the fold of a critical manifiold. We find a Hopf bifurcation as the rate parameter increases in the reduced co-moving system. This implies the growth of a…
Nonlinear dynamical systems may be exposed to tipping points, critical thresholds at which small changes in the external inputs or in the systems parameters abruptly shift the system to an alternative state with a contrasting dynamical…
We consider a model for substrate-depletion oscillations in genetic systems, based on a stochastic differential equation with a slowly evolving external signal. We show the existence of critical transitions in the system. We apply two…
Aspects of cell metabolism are modeled by ordinary differential equations describing the change of intracellular chemical concentrations. There is a correspondence between this dynamical system and a complex network. As in the classic…
In this paper we analyze a coupled system between a transport equation and an ordinary differential equation with time delay (which is a simplified version of a model for kidney blood flow control). Through a careful spectral analysis we…
We investigate delay effects on dominant transition pathways (DTP) between metastable states of stochastic systems. A modified version of the Maier-Stein model with linear delayed feedback is considered as an example. By a stability…
The synthetic construction of intracellular circuits is frequently hindered by a poor knowledge of appropriate kinetics and precise rate parameters. Here, we use generalized modeling (GM) to study the dynamical behavior of topological…
Diverse complex dynamical systems are known to exhibit abrupt regime shifts at bifurcation points of the saddle-node type. The dynamics of most of these systems, however, have a stochastic component resulting in noise driven regime shifts…
In multicellular organisms, several cell states coexist. For determining each cell type, cell-cell interactions are often essential, in addition to intracellular gene expression dynamics. Based on dynamical systems theory, we propose a…
Background: Genotype-phenotype maps provide a meaningful filtration of sequence space and RNA secondary structures are particular such phenotypes. Compatible sequences i.e.~sequences that satisfy the base pairing constraints of a given RNA…
Fast-slow dynamical systems have subsystems that evolve on vastly different timescales, and bifurcations in such systems can arise due to changes in any or all subsystems. We classify bifurcations of the critical set (the equilibria of the…
Cells often exhibit different and stable phenotypes from the same DNA sequence. Robustness and plasticity of such cellular states are controlled by diverse transcriptional and epigenetic mechanisms, among them the modification of…
Hopf bifurcation in networks of coupled ODEs creates periodic states in which the relative phases of nodes are well defined near bifurcation. When the network is a fully inhomogeneous nearest-neighbour coupled unidirectional ring, and node…