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We expose some selected topics concerning the instability of the action variables in a priori unstable Hamiltonian systems, and outline a new strategy that may allow to apply these methods to a priori stable systems.
Understanding how biological homochirality emerged remains a challenge for the researchers interested in the origin of life. During the last decades, stable non-racemic steady states of nonequilibrium chemical systems have been discussed as…
Because organisms synthesize component molecules at rates that reflect those molecules' adaptive utility, we expect a population of biota to leave a distinctive chemical signature on their environment that is anomalous given the local…
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, we study a nonlinear boundary diffusion equation of porous medium type arising from a boundary control problem. We give a complete and sharp characterization of the asymptotic behavior of its solutions, and prove the…
This paper deals with system with $n$ identical elements and one repairing device. While one element working other ones stay in reserve. The distribution of element working and repairing times are supposed to be exponential. Here we obtain…
In this study, a spatially distributed reaction-diffusion-advection (RDA) model with harvesting is investigated to signify the outcome of a competition between two competing species in a heterogeneous environment. The study builds upon the…
Planar wave trains are traveling wave solutions whose wave profiles are periodic in one spatial direction and constant in the transverse direction. In this paper, we investigate the stability of planar wave trains in reaction-diffusion…
Turing instabilities of reaction-diffusion systems can only arise if the diffusivities of the chemical species are sufficiently different. This threshold is unphysical in most systems with $N=2$ diffusing species, forcing experimental…
This paper considers the problem of robust stability for a class of uncertain nonlinear quantum systems subject to unknown perturbations in the system Hamiltonian. The nominal system is a linear quantum system defined by a linear vector of…
A general system of several ordinary differential equations coupled with a reaction-diffusion equation in a bounded domain with zero-flux boundary condition is studied in the context of pattern formation. These initial-boundary value…
We discuss stationary concentrations of reactants in an A + B -> 0 reaction under subdiffusion and show that they are described by stationary reaction-diffusion equations with a nonlinear diffusion term. We consider stationary profiles of…
We analyze a reaction-diffusion system describing the growth of microbial species in a model of flocculation type that arises in biology. Existence of global classical positive solutions is proved under general growth assumptions, with…
We consider biochemical reaction chains and investigate how random external fluctuations, as characterized by variance and coefficient of variation, propagate down the chains. We perform such a study under the assumption that the number of…
The combined influence of oscillatory excitations and multiplicative stochastic perturbations of white noise type on isochronous systems in the plane is investigated. It is assumed that the intensity of perturbations decays with time and…
This work focuses on stability of regime-switching diffusions consisting of continuous and discrete components, in which the discrete component switches in a countably infinite set and its switching rates at current time depend on the…
We present a computational framework to investigate steady state distributions and perform stability analysis for random ordinary differential equations driven by parameter uncertainty. Using the nonlinear Rosenzweig McArthur predator prey…
We propose a systematic method to derive the asymptotic behaviour of the persistence distribution, for a large class of stochastic processes described by a general Fokker-Planck equation in one dimension. Theoretical predictions are…
Output feedback stabilization of control systems is a crucial issue in engineering. Most of these systems are not uniformly observable, which proves to be a difficulty to move from state feedback stabilization to dynamic output feedback…
We analyse the asymptotic behaviour of a nonlinear mathematical model of cellular proliferation which describes the production of blood cells in the bone marrow. This model takes the form of a system of two maturity structured partial…