1,720,964 research outputs found
Stability of a Continuous Reaction-Diffusion Cournot-Kopel Duopoly Game Model
No full textIn order to take into account the territory in which the outputs are in the market and the time-depending firms' strategies, the discrete Cournot duopoly game (with adaptive expectations, modeled by Kopel) is generalized through a non autonomous reaction-diffusion binary system of PDEs, with self and cross diffusion terms. Linear and nonlinear asymptotic L2-stability, via the Liapunov Direct Methot and a nonautonomous energy functional, are investigated
Longtime behavior of vertical throughflows for binary mixtures in porous layers
No full textNon-linear stability of vertical throughflows in porous layers, uniformly heated and salted from below, is analyzed. The definitively boundedness of the solutions (existence of absorbing sets in the phase space) is proved. Conditions guaranteeing global non-linear asymptotic stability have been found. In closed form, the critical Rayleigh number has been found
Influence of diffusion on the stability of a full Brusselator model
No full textThe classic Brusselator model consists of four reactions involving six components A, B, D, E, X, Y. In a typical run, the final products and are removed instantly, while, the concentrations of the reactants A and B are kept constant. Then, the classic Brusselator model consisting of two equations for the intermediate X and Y is obtained. When the component B is not considered constant, it is added to the mixture and the so-called full Brusselator model is considered. In this paper, the full Brusselator model is studied. In particular, the boundedness of solutions and the effect of diffusion on the linear stability
is analyzed. Moreover, sufficient conditions ensuring that the unique steady state, unstable (stable) in the ODEs system, becomes stable (unstable) in presence of diffusion, are performed and a first nonlinear stability result is obtained
On the dynamics of an intraguild predator-prey model
No full textAn intraguild predator-prey model with a carrying capacity proportional to the biotic resource, is generalized by introducing a Holling type II functional response. The longtime behavior of solutions is analyzed and, in particular, absorbing sets in the phase space are determined. The existence of biologically meaningful equilibria (boundary and internal equilibria) has been investigated. Linear and nonlinear stability conditions for biologically meaningful equilibria are performed. Finally, numerical simulations on different regimes of coexistence and extinction of the involved populations have been shown
On the stability of vertical constant throughflows for binary mixtures in porous layers
No full textA system modeling fluid motions in horizontal porous layers, uniformly heated from below and salted from above by one salt, is analyzed. The definitely boundedness of solutions (existence of absorbing sets) is proved. Necessary and sufficient conditions ensuring the linear stability of a vertical constant throughflow have been obtained, via a new approach. Moreover, conditions guaranteeing the global nonlinear asymptotic stability are determined
Nonlinear stability analysis of a chemical reaction–diffusion system
No full textA reaction–diffusion model, known as the Sel’kov–Schnakenberg model, is considered. The nonlinear stability of the constant steady state is studied by using a special Liapunov functional and a maximum principle for regular solutions
Turing Instability and Spatial Pattern Formation in a Model of Urban Crime
Full text linkA nonlinear crime model is generalized by introducing self- and cross-diffusion terms. The effect of diffusion on the stability of non-negative constant steady states is applied. In particular, the cross-diffusion-driven instability, called Turing instability, is analyzed by linear stability analysis, and several Turing patterns driven by the cross-diffusion are studied through numerical investigations. When the Turing–Hopf conditions are satisfied, the type of instability highlighted in the ODE model persists in the PDE system, still showing an oscillatory behavior
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