Open AccessJournal Article
Modeling Complex Systems by Functional Subsystems Representation and Thermostatted-KTAP Methods
TL;DR: This paper is concerned with suitable developments of the methods of mathematical kinetic theory for active particles for the modeling of complex systems splitted in functional subsystems and constrained to maintain constant some macroscopic quantities.
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Abstract: In the last two decades the mathematical modeling of real-world complex systems has received much attention These sys- tems are composed by a high number of interacting entities which are able to express a specific strategy In order to reduce complexity, the whole system is decomposed in different subsystems that are sets of heterogeneous entities having the ability of exp ressing the same function The microscopic interactions among the functional subsystems generate the emerging behaviors that are typical of the com- plex systems This paper is concerned with suitable developments of the methods of mathematical kinetic theory for active particles for the modeling of complex systems splitted in functional subsystems and constrained to maintain constant some macroscopic quantities
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Citations
Kinetic models coupled with Gaussian thermostats: macroscopic frameworks
TL;DR: In this article, the authors deal with the modeling of complex systems composed of a large number of elements grouped into different functional subsystems and derive evolution equations for the macroscopic variables (density and momentum) from the underlying description at the microscopic scale delivered by the thermostatted kinetic models.
Existence of stationary solutions in kinetic models with Gaussian thermostats
TL;DR: In this article, the existence of stationary solutions proof is proved by fixed point and measure theory arguments, and the main result is gained by fixed-point and measure-based arguments.
29
High-order moments conservation in thermostatted kinetic models
TL;DR: The derived framework that constitutes a new paradigm for the derivation of specific models in the applied sciences, is analytically investigated and the global in time existence and uniqueness of the solution to the relative Cauchy problem is proved.
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Existence of limit cycles in the Solow model with delayed-logistic population growth.
Carlo Bianca,Luca Guerrini +1 more
TL;DR: The Solow model is further improved by inserting the time delay into the logistic population growth rate and it is proved that the system loses its stability and a Hopf bifurcation occurs when time delay passes through critical values.
The Role of Nonconservative Interactions in the Asymptotic Limit of Thermostatted Kinetic Models
TL;DR: In this article, the asymptotic analysis of space-velocity dependent thermostatted kinetic frameworks is studied, which include conservative, non-conservative and stochastic operators.
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