相关论文: Excitability in a Model with a Saddle-Node Homocli…
We explore an embryonic heart model that couples electrophysiology and muscle-force generation to flow induced using a $2D$ fluid-structure interaction framework based on the immersed boundary method. The propagation of action potentials…
Bifurcations mark qualitative changes of long-term behavior in dynamical systems and can often signal sudden ("hard") transitions or catastrophic events (divergences). Accurately locating them is critical not just for deeper understanding…
Astounding properties of biological sensors can often be mapped onto a dynamical system in the vicinity a bifurcation. For mammalian hearing, a Hopf bifurcation description has been shown to work across a whole range of scales, from…
Spatio-temporal extensions of familiar compartment models for disease transmission incorporating diffusive behavior, or interactions between individuals at separate locations, are explored. The models considered have the character of…
We propose a new class of tight-binding models where a flat band is either gapped from or crossing right through a dispersive band on two-band (i.e., two sites/unit cell) tetragonal and honeycomb lattices. By imposing a condition on the…
This paper explores the classification of parameter spaces for reaction-diffusion systems of two chemical species on stationary domains. The dynamics of the system are explored both in the absence and presence of diffusion. The parameter…
In this paper, we consider a continuous-time model with discrete and dis-tributed delays to describe how two pieces of information interact in online social networks. Sufficient conditions are carried out to illustrate the stability of each…
This study investigates the existence and stability of limit cycles resulting from self-excited oscillations in linear multi-degree-of-freedom systems subjected to discontinuous, state-dependent forcing. Using the method of averaging and…
This paper proposes a conceptual model for the onset of a stable torus near a saddle-focus equilibrium. This bifurcation scenario is typical of slow-fast systems that generate elliptic bursting in a variety of neuronal models in…
A four-dimensional mathematical model of the hypothalamus-pituitary-adrenal (HPA) axis is investigated, incorporating the influence of the GR concentration and general feedback functions. The inclusion of distributed time delays provides a…
We analytically derive mean-field models for all-to-all coupled networks of heterogeneous, adapting, two-dimensional integrate and fire neurons. The class of models we consider includes the Izhikevich, adaptive exponential, and quartic…
We investigate dynamics and bifurcations in a mathematical model that captures electrochemical experiments on arrays of microelectrodes. In isolation, each individual microelectrode is described by a one-dimensional unit with a bistable…
We analytically derive an equation describing vesicle evolution in a fluid where some stationary flow is excited regarding that the vesicle shape is close to a sphere. A character of the evolution is governed by two dimensionless…
Demixing of binary fluids subjected to slow temperature ramps shows repeated waves of nucleation which arise as a consequence of the competition between generation of supersaturation by the temperature ramp and relaxation of supersaturation…
We examine the evolution of a bistable reaction in a one-dimensional stretching flow, as a model for chaotic advection. We derive two reduced systems of ordinary differential equations (ODE's) for the dynamics of the governing…
The paper discusses the use of amplitude equations to describe the spatio-temporal dynamics of a chemical reaction-diffusion system based on an Oregonator model of the Belousov-Zhabotinsky reaction. Sufficiently close to a supercritical…
This article aims to provide insights into the qualitative analysis of some nonlinear Reaction-Diffusion (RD) systems arising in Neuroscience. We first introduce a non-homogeneous FitzHugh-Nagumo (nhFHN) featuring excitability and…
We apply spatial dynamical-systems techniques to prove that certain spatiotemporal patterns in reversible reaction-diffusion equations undergo snaking bifurcations. That is, in a narrow region of parameter space, countably many branches of…
Cochlea displays complex and highly nonlinear behavior in response to wide-ranging auditory stimuli. While there have been many recent advancements in the modeling of cochlear dynamics, it remains unclear what mathematical structures…
We investigate the relation between the stationary probability distribution of chemical reaction systems and the convective field derived from the chemical Fokker-Planck equation (CFPE) by comparing predictions of the convective field to…