Existence and uniqueness of nonequilibrium stationary solutions in discrete thermostatted models

Bianca, Carlo; Menale, Marco

doi:10.1016/j.cnsns.2019.01.026

Cited by 10 publications

(11 citation statements)

References 22 publications

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“…Some of these models are formulated within the so-called thermostatted KTAP developed recently in a series of papers, see for example, References [36,[82][83][84][85][86][87][88][89][90] and the references therein.…”

Section: Examplesmentioning

confidence: 99%

Mathematical Analysis of an Autoimmune Diseases Model: Kinetic Approach

Kolev

2019

Mathematics

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A new mathematical model of a general autoimmune disease is presented. Basic information about autoimmune diseases is given and illustrated with examples. The model is developed by using ideas from the kinetic theory describing individuals expressing certain functions. The modeled problem is formulated by ordinary and partial equations involving a variable for a functional state. Numerical results are presented and discussed from a medical view point.

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Section: Examplesmentioning

confidence: 99%

Mathematical Analysis of an Autoimmune Diseases Model: Kinetic Approach

Kolev

2019

Mathematics

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“…The existence of nonequilibrium stationary solutions g ∈R 2 f was proven in [14], under Assumptions H1-H2 and:…”

Section: The Discrete Thermostatted Frameworkmentioning

confidence: 99%

“…In particular, in [14], it was proven that the nonequilibrium stationary solution is unique if the following constraint on the force field F(t) = (F, F, . .…”

Section: The Discrete Thermostatted Frameworkmentioning

confidence: 99%

“…Recently, the discrete thermostatted kinetic theory was proposed in [13,14] for the modeling and analysis of a far from equilibrium complex system; applications to biology [15,16] and crowd dynamics have been developed [17]. According to this theory, the complex system is divided into different functional subsystems composed by particles expressing the same task, which is usually a strategy.…”

Section: Introductionmentioning

confidence: 99%

“…The present paper is devoted to a further mathematical analysis of the discrete thermostatted kinetic theory framework proposed in [13]. The conditions of the existence and uniqueness of the nonequilibrium stationary solution were investigated in [14]. This paper provides the mathematical proof that the solutions of the discrete thermostatted kinetic theory framework approach the nonequilibrium stationary solutions when the time goes to infinity.…”

Section: Introductionmentioning

confidence: 99%

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A Convergence Theorem for the Nonequilibrium States in the Discrete Thermostatted Kinetic Theory

Bianca

Menale

2019

Mathematics

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The existence and reaching of nonequilibrium stationary states are important issues that need to be taken into account in the development of mathematical modeling frameworks for far off equilibrium complex systems. The main result of this paper is the rigorous proof that the solution of the discrete thermostatted kinetic model catches the stationary solutions as time goes to infinity. The approach towards nonequilibrium stationary states is ensured by the presence of a dissipative term (thermostat) that counterbalances the action of an external force field. The main result is obtained by employing the Discrete Fourier Transform (DFT).

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A kinetic theory approach to modeling prey–predator ecosystems with expertise levels: analysis, simulations and stability considerations

Menale,

Venturino

2024

Comp. Appl. Math.

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In this paper a kinetic modeling approach for an ecological system is proposed, based on the prey–predator structure in terms of individuals experience. Specifically, a system of nonlinear kinetic equations is formulated using standard tools. Both conservative and nonconservative events are considered since proliferative/destructive rates and an external force field occur. These results are compared to the ones of the classical theory of dynamical system to show their consistency. In addition to a first local analytical result, some numerical simulations are performed. The results thus obtained ensure that the kinetic model behaves in a way consistent with other similar ecological models formulated by dynamical systems, involving ordinary differential equations with lumped dependent variables. For each simulation, stationary solutions are shown. Moreover, oscillations appear for some values of the parameters of the ecological system, and this suggests that bifurcations may appear.

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Existence and uniqueness of nonequilibrium stationary solutions in discrete thermostatted models

Cited by 10 publications

References 22 publications

Mathematical Analysis of an Autoimmune Diseases Model: Kinetic Approach

Mathematical Analysis of an Autoimmune Diseases Model: Kinetic Approach

A Convergence Theorem for the Nonequilibrium States in the Discrete Thermostatted Kinetic Theory

A kinetic theory approach to modeling prey–predator ecosystems with expertise levels: analysis, simulations and stability considerations

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