Zobrazeno 1 - 10
of 559
pro vyhledávání: '"37G15"'
We present a detailed study of a scalar differential equation with threshold state-dependent delayed feedback. This equation arises as a simplification of a gene regulatory model. There are two monotone nonlinearities in the model: one describes the
Externí odkaz:
http://arxiv.org/abs/2410.13092
Autor:
Ruschel, Stefan, Giraldo, Andrus
Computing the spectrum and stability of traveling waves in spatially discrete systems quickly becomes unfeasible with increasing system size. We present a framework for effectively determining the spectrum and stability of traveling waves in discrete
Externí odkaz:
http://arxiv.org/abs/2409.12736
When a dynamical system is subject to a periodic perturbation, the averaging method can be applied to obtain an autonomous leading order `guiding system', placing the time dependence at higher orders. Recent research focused on investigating invarian
Externí odkaz:
http://arxiv.org/abs/2409.11054
Motivated by numerical continuation studies of coupled mechanical oscillators, we investigate branches of localized time-periodic solutions of one-dimensional chains of coupled oscillators. We focus on Ginzburg-Landau equations with nonlinearities of
Externí odkaz:
http://arxiv.org/abs/2409.07546
Quorum sensing orchestrates bacterial communication, which is vital for bacteria's population behaviour. We propose a mathematical model that unveils chaotic dynamics within quorum sensing networks, challenging predictability. The model considers the
Externí odkaz:
http://arxiv.org/abs/2409.02764
This paper addresses the perturbation of higher-dimensional non-smooth autonomous differential systems characterized by two zones separated by a codimension-one manifold, with an integral manifold foliated by crossing periodic solutions. Our primary
Externí odkaz:
http://arxiv.org/abs/2409.01851
The FitzHugh-Nagumo system is a $4$-parameter family of $3$D vector field used for modeling neural excitation and nerve impulse propagation. The origin represents a Hopf-zero equilibrium in the FitzHugh-Nagumo system for two classes of parameters. In
Externí odkaz:
http://arxiv.org/abs/2408.12771
Autor:
Simpson, David J. W.
The border-collision normal form is a piecewise-linear family of continuous maps that describe the dynamics near border-collision bifurcations. Most prior studies assume each piece of the normal form is invertible, as is generic from an abstract view
Externí odkaz:
http://arxiv.org/abs/2408.04790
Autor:
Edelman, Mark
In regular dynamics, discrete maps are model presentations of discrete dynamical systems, and they may approximate continuous dynamical systems. Maps are used to investigate general properties of dynamical systems and to model various natural and soc
Externí odkaz:
http://arxiv.org/abs/2408.00134
Autor:
Glendinning, P. A., Simpson, D. J. W.
The border-collision normal form describes the local dynamics in continuous systems with switches when a fixed point intersects a switching surface. For one-dimensional cases where the bifurcation creates or destroys only fixed points and period-two
Externí odkaz:
http://arxiv.org/abs/2407.16865