We focus on the qualitative analysis of a reaction-diffusion with spatial heterogeneity. The system is a generalization of the well known FitzHugh-Nagumo system in which the excitability parameter is space dependent. This heterogeneity allows to exhibit concomitant stationary and oscillatory phenomena. We prove the existence of an Hopf bifurcation and determine an equation of the center-manifold in which the solution asymptotically evolves. Numerical simulations illustrate the phenomenon.
The diffusive predator-prey model with Ivlev functional response is considered under homogeneous Dirichlet boundary conditions. Firstly, we investigate the bifurcation of positive solutions and derive the multiplicity result for γ suitably large. Furthermore, a range of parameters for the uniqueness of positive solutions is described in one dimension. The method we used is based on a comparison principle, Leray-Schauder degree theory, global bifurcation theory and generalized maximum principle. MSC: 35K57
This paper is intended to introduce the subtractive derivations and study some of their algebraic properties on R
l
-monoids. Also, we give some characterizations of subtractive derivations on the Gödel center. Moreover, Gödel algebras are characterized by a fixed set of subtractive derivations. Finally, we discuss the relationship between subtractive derivations and other derivations for R
l
-monoids. These results of the paper can provide the common properties of subtractive derivations in the t-norm-based fuzzy logical algebras.
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