Related papers: Finding Eigenvalues the Rupert Way
We study the spectral stability of travelling and stationary front and pulse solutions in a class of degenerate reaction-diffusion systems. We characterise the essential spectrum of the linearised operator in full generality and identify…
We demonstrate a geometrically inspired technique for computing Evans functions for the linearised operators about travelling waves. Using the examples of the F-KPP equation and a Keller-Segel model of bacterial chemotaxis, we produce an…
We prove existence and uniqueness of travelling waves for a reaction-diffusion system coupling a classical reaction-diffusion equation in a strip with a diffusion equation on a line. To do this we use a continuation method which leads to…
Context. The study of linear waves and instabilities is necessary to understand the physical evolution of an atmosphere, and can provide physical interpretation of the complex flows found in simulations performed using Global Circulation…
Closed combustion devices like gas turbines and rockets are prone to thermoacoustic instabilities. Design engineers in the industry need tools to accurately identify and remove instabilities early in the design cycle. Many different…
We consider a free boundary model of epithelial cell migration with logistic growth and nonlinear diffusion induced by mechanical interactions. Using numerical simulations, phase plane and perturbation analysis, we find and analyse…
Three-dimensional geophysical fluids support both internal and boundary-trapped waves. To obtain the normal modes in such fluids we must solve a differential eigenvalue problem for the vertical structure (for simplicity, we only consider…
We study stability of monostable waves for reaction-diffusion systems. When the solution is initially close to a fast wave profile in optimal topology, we prove convergence to a shifted profile. The proof relies on explicit resolvent…
We consider the stability of position control of traveling waves in reaction-diffusion system as proposed in {[}J. L\"ober, H. Engel, arXiv:1304.2327{]}. Instead of analyzing the controlled reaction-diffusion system, stability is studied on…
In this paper, we investigate the existence, uniqueness, and spectral stability of traveling waves arising from a single threshold neural field model with one spatial dimension, a Heaviside firing rate function, axonal propagation delay,…
Changes in environmental or system parameters often drive major biological transitions, including ecosystem collapse, disease outbreaks, and tumor development. Analyzing the stability of steady states in dynamical systems provides critical…
We give sufficient conditions for the existence of positive travelling wave solutions for multi-dimensional autonomous reaction-diffusion systems with distributed delay. To prove the existence of travelling waves, we give an abstract…
We study the traveling wave solutions to a reaction diffusion system modeling the public goods game with altruistic behaviors. The existence of the waves is derived through monotone iteration of a pair of classical upper- and lower…
Partial differential equations endowed with a Hamiltonian structure, like the Korteweg--de Vries equation and many other more or less classical models, are known to admit rich families of periodic travelling waves. The stability theory for…
A new method for the stability assessment of inverter-based microgrids is presented in this paper. Directly determining stability boundaries by searching the multidimensional space of inverters' droop gains is a computationally prohibitive…
Nonreciprocal interactions, in which action-reaction symmetry is broken, provide a powerful route to collective dynamics that cannot be captured by equilibrium free-energy minimisation. Here, we introduce and analyse a two-species…
We perform a linear stability analysis of three-layer radial porous media and Hele-Shaw flows with variable viscosity in the middle layer. A nonlinear change of variables results in an eigenvalue problem that has time-dependent coefficients…
We study stability of travelling wave solutions to Korteweg--de Vries type equations which has the fractional dispersion and integer-indices double power nonlinearities. It may depend on parity combinations of the two indices and the…
In this work we study the orbital stability of periodic traveling-wave solutions for dispersive models. The study of traveling waves started in the mid-18th century when John S. Russel established that the flow of water waves in a shallow…
In order to understand the nonlinear stability of many types of time-periodic travelling waves on unbounded domains, one must overcome two main difficulties: the presence of embedded neutral eigenvalues and the time-dependence of the…