相关论文: Structural conditions for saddle-node bifurcations…

In this article we construct the parameter region where the existence of a homoclinic orbit to a zero equilibrium state of saddle type in the Lorenz-like system will be analytically proved in the case of a nonnegative saddle value. Then,…

In this paper, we present an algorithm for deriving the normal forms of Bautin bifurcations in reaction-diffusion systems with time delays and Neumann boundary conditions. On the center manifold near a Bautin bifurcation, the first and…

We determine conditions under which a random biochemical system is likely to contain a subsystem that is both autocatalytic and able to survive on some ambient `food' source. Such systems have previously been investigated for their…

Information processing in the brain crucially depends on encoding properties of single neurons, with particular relevance of the spike-generation mechanism. The latter hinges upon the bifurcation type at the transition point between resting…

In most natural sciences there is currently the insight that it is necessary to bridge gaps between different processes which can be observed on different scales. This is especially true in the field of chemical reactions where the…

Many biological systems, such as metabolic pathways, exhibit bistability behavior: these biological systems exhibit two distinct stable states with switching between the two stable states controlled by certain conditions. Since…

We perform both analytical and numerical bifurcation analysis of a forest-grassland ecosystem model coupled with human interaction. The model consists of two nonlinear ordinary differential equations incorporating the human perception of…

Our ability to control complex systems is a fundamental challenge of contemporary science. Recently introduced tools to identify the driver nodes, nodes through which we can achieve full control, predict the existence of multiple control…

Particles that are catalytically-active and chemotactic can interact through the concentration fields upon which they act, which in turn may lead to wide-scale spatial self-organization. When these active particles interact through several…

Models of biochemical networks are usually presented as connected graphs where vertices indicate proteins and edges are drawn to indicate activation or inhibition relationships. These diagrams are useful for drawing qualitative conclusions…

Transitions between multiple stable states of nonlinear systems are ubiquitous in physics, chemistry, and beyond. Two types of behaviors are usually seen as mutually exclusive: unpredictable noise-induced transitions and predictable…

Biological networks have evolved to be highly functional within uncertain environments while remaining extremely adaptable. One of the main contributors to the robustness and evolvability of biological networks is believed to be their…

In this thesis, we have studied the large scale structure and system level dynamics of certain biological networks using tools from graph theory, computational biology and dynamical systems. We study the structure and dynamics of large…

Oscillatory dynamics are ubiquitous in biological networks. Possible sources of oscillations are well understood in low-dimensional systems, but have not been fully explored in high-dimensional networks. Here we study large networks…

We discuss the transition paths in a coupled bistable system consisting of interacting multiple identical bistable motifs. We propose a simple model of coupled bistable gene circuits as an example, and show that its transition paths are…

Reaction networks have become a major modelling framework in the biological sciences from epidemiology and population biology to genetics and cellular biology. In recent years, much progress has been made on stochastic reaction networks…

Scaling analysis exploiting timescale separation has been one of the most important techniques in the quantitative analysis of nonlinear dynamical systems in mathematical and theoretical biology. In the case of enzyme catalyzed reactions,…

We define a subclass of Chemical Reaction Networks called Post-Translational Modification systems. Important biological examples of such systems include MAPK cascades and two-component systems which are well-studied experimentally as well…

Signal transduction within biological cells is governed by networks of interacting proteins. Communication between these proteins is mediated by signaling molecules which bind to receptors and induce stochastic transitions between different…

In chemical reaction network theory, ordinary differential equations are used to model the temporal change of chemical species concentration. As the functional form of these ordinary differential equations systems is derived from an…