Abstract
This paper treats interaction between finitely many particles where the future state of each particle is obtained from the present states of all other particles by a positive linear combination with time variant coefficients. The main result provides conditions for a common globally asymptotically stable equilibrium to exist. These conditions are, in particular, satisfied if the particles show slowly decaying interation. Since “particles” can be many things, there are many applications, for example, heat diffusion in an inhomogeneous medium, a many body problem under pseudo-gravity and consensus formation under bounded confidence.
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Krause, U. Positive Particle Interaction. In: Benvenuti, L., De Santis, A., Farina, L. (eds) Positive Systems. Lecture Notes in Control and Information Science, vol 294. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44928-7_27
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DOI: https://doi.org/10.1007/978-3-540-44928-7_27
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40342-5
Online ISBN: 978-3-540-44928-7
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