Search

In this study, a synchronization problem for spatio-temporal partial differential systems is addressed and researched within a subjectivist framework. In light of Lyapunov direct method and some proposed nonlinear controllers, a new scheme is established to accomplish a full synchronization between two reaction–diffusion systems of integer- and fractional-order. In particular, a novel vector-valued control law is analytically derived to attain the desired synchronization between two chemical models, namely, the Lengyel–Epstein and Gray–Scott models. To validate the obtained theoretical results, further numerical simulations are carried out in 2D and 3D configurations. [ABSTRACT FROM AUTHOR]

In this paper, five different models for five different kinds of diseases occurring in wildlife populations are introduced. In all models, a logistic growth term is taken into account and the disease is transmitted to the susceptible population indirectly through an environment reservoir. The time evolution of these diseases is described together with its spatial propagation. The character of spatial homogeneous equilibria against the uniform and non-uniform perturbations together with the occurrence of Hopf bifurcations are discussed through a linear stability analysis. No Turing instability is observed. The partial differential field equations are also integrated numerically to validate the stability results herein obtained and to extract additional information on the temporal and spatial behavior of the different diseases. [ABSTRACT FROM AUTHOR]

We present a variational formulation for the Kardar–Parisi–Zhang (KPZ) equation that leads to a thermodynamic-like potential for the KPZ as well as for other related kinetic equations. For the KPZ case, with the knowledge of such a potential we prove some global shift invariance properties previously conjectured by other authors. We also show a few results about the form of the stationary probability distribution function for arbitrary dimensions. The procedure used for KPZ was extended in order to derive more general forms of such a functional leading to other nonlinear kinetic equations, as well as cases with density dependent surface tension. [ABSTRACT FROM AUTHOR]

Oscillating localized structures are studied for a simple reaction–diffusion model from an analytical point of view. The result is a particle solution which acts as a source of traveling waves. The analytical expressions obtained are in good agreement with direct numerical simulations. [ABSTRACT FROM AUTHOR]