Zobrazeno 1 - 10
of 93
pro vyhledávání: '"Jaramillo, Gabriela"'
Autor:
Jaramillo, Gabriela
We prove existence of spiral waves in oscillatory media with nonlocal coupling. Our starting point is a nonlocal complex Ginzburg-Landau (cGL) equation, rigorously derived as an amplitude equation for integro-differential equations undergoing a Hopf
Externí odkaz:
http://arxiv.org/abs/2401.15226
The Gray-Scott model is a set of reaction-diffusion equations that describes chemical systems far from equilibrium. Interest in this model stems from its ability to generate spatio-temporal structures, including pulses, spots, stripes, and self-repli
Externí odkaz:
http://arxiv.org/abs/2212.10648
The May--Leonard model was introduced to examine the behavior of three competing populations where rich dynamics, such as limit cycles and nonperiodic cyclic solutions, arise. In this work, we perturb the system by adding the capability of global mut
Externí odkaz:
http://arxiv.org/abs/2210.04342
Autor:
Jaramillo, Gabriela
We study the existence of target patterns in oscillatory media with weak local coupling and in the presence of an impurity, or defect. We model these systems using a viscous eikonal equation posed on the plane, and represent the defect as a perturbat
Externí odkaz:
http://arxiv.org/abs/2207.01804
Autor:
Jaramillo, Gabriela
Biological and physical systems that can be classified as oscillatory media give rise to interesting phenomena like target patterns and spiral waves. The existence of these structures has been proven in the case of systems with local diffusive intera
Externí odkaz:
http://arxiv.org/abs/2103.14940
In this paper we develop a numerical scheme based on quadratures to approximate solutions of integro-differential equations involving convolution kernels, $\nu$, of diffusive type. In particular, we assume $\nu$ is symmetric and exponentially decayin
Externí odkaz:
http://arxiv.org/abs/2008.02865
The goal of this paper is to describe the oscillatory microstructure that can emerge from minimizing sequences for nonconvex energies. We consider integral functionals that are defined on real valued (scalar) functions $u(x)$ which are nonconvex in t
Externí odkaz:
http://arxiv.org/abs/1912.03360
Publikováno v:
Nonlinearity, vol. 31, no. 9, pg. 4162 (2018)
We analyze the effect of adding a weak, localized, inhomogeneity to a two dimensional array of oscillators with nonlocal coupling. We propose and also justify a model for the phase dynamics in this system. Our model is a generalization of a viscous e
Externí odkaz:
http://arxiv.org/abs/1706.00524
Publikováno v:
Proceedings of the Royal Society of Edinburgh: Section A Mathematics 149 (2019) 131-168
We study the effect of algebraically localized impurities on striped phases in one space-dimension. We therefore develop a functional-analytic framework which allows us to cast the perturbation problem as a regular Fredholm problem despite the presen
Externí odkaz:
http://arxiv.org/abs/1604.07786
Publikováno v:
SIAM Journal on Applied Mathematics; 2024, Vol. 84 Issue 3, p856-889, 34p