Related papers: The non linear dynamics of retinal waves
Inspired by creation of a fast exchange-only qubit (Medford et al., Phys. Rev. Lett., 111, 050501 (2013)), we develop a theory describing the nonlinear dynamics of two such qubits that are capacitively coupled, when one of them is driven…
We examine the dynamical evolution of the state of a neurone, with particular care to the non-equilibrium nature of the forces influencing its movement in state space. We combine non-equilibrium statistical mechanics and dynamical systems…
We investigate the stability and nonlinear local dynamics of spectrally stable wave trains in reaction-diffusion systems. For each $N\in\mathbb{N}$, such $T$-periodic traveling waves are easily seen to be nonlinearly asymptotically stable…
In this paper, a general model of wireless channels is established based on the physics of wave propagation. Then the problems of inverse scattering and channel prediction are formulated as nonlinear filtering problems. The solutions to the…
The nervous system displays a variety of rhythms in both waking and sleep. These rhythms have been closely associated with different behavioral and cognitive states, but it is still unknown how the nervous system makes use of these rhythms…
It is shown, by means of numerical simulations, that intercellular spiral waves of calcium can be initiated in a network of coupled cells as a result of a de-synchronization between Ca2+ oscillations in two domains. No artificial…
Resonant electron interaction with whistler-mode chorus waves is recognized as one of the main drivers of radiation belt dynamics. For moderate wave intensity, this interaction is well described by quasi-linear theory. However, recent…
An isotropic elastic half space is prestrained so that two of the principal axes of strain lie in the bounding plane, which itself remains free of traction. The material is subject to an isotropic constraint of arbitrary nature. A surface…
Nonlinear dynamics of two biomolecules is studied. These are a microtubule and DNA molecule. Two mathematical procedures are explained, yielding to three kinds of solitary waves moving through the systems. These waves are kinks, modulated…
We use perturbation theory and bifurcation theory to analyze the dynamical behavior of resonances, associated to a model describing a particle moving within a ring around a celestial object. The central body is modeled as a homogeneous…
The study of granular crystals, metamaterials that consist of closely packed arrays of particles that interact elastically, is a vibrant area of research that combines ideas from disciplines such as materials science, nonlinear dynamics,…
Flow networks are essential for both living organisms and enginneered systems. These networks often present complex dynamics controlled, at least in part, by their topology. Previous works have shown that topologically complex networks…
The presence of one or more species at some spatial locations but not others is a central matter in ecology. This phenomenon is related to ecological pattern formation. Nonlocal interactions can be considered as one of the mechanisms…
We developed a nonlinear differential equation model to explore the dynamics of relapse phenomena. Our incidence rate function is formulated, taking inspiration from recent adaptive algorithms. It incorporates contact behavior for…
We study mechanisms for wavenumber selection in a minimal model for run-and-tumble dynamics. We show that nonlinearity in tumbling rates induces the existence of a plethora of traveling- and standing-wave patterns, as well as a subtle…
Recent experiments by Kantsler et. al. (2007) have shown that the relaxational dynamics of a vesicle in external elongation flow is accompanied by the formation of wrinkles on a membrane. Motivated by these experiments we present a theory…
We review the scattering from non-linear interfaces containing buckling elastic beams. An illustrative example is discussed here of scattering of linear elastic pressure waves from a two-mass system connected by a non-linear structured…
We determine the modulational stability of standing waves with small group velocity in quasi-onedimensional systems slightly above the threshold of a supercritical Hopf bifurcation. The stability limits are given by two different…
In this work, we study the wave propagation in a recently proposed acoustic structure, the locally resonant granular crystal. This structure is composed of a one-dimensional granular crystal of hollow spherical particles in contact,…
We numerically investigate the phase separation dynamics of the non-reciprocal Allen-Cahn model in which two non-conserved order parameters are coupled. The system exhibits several dynamical patterns such as the randomly oscillating phase…