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Fixed points of complex systems with attractive interaction. (English) Zbl 1389.37057

The authors study the behavior of complex dynamical systems describing an attractive interaction between two opponents. As in a number of previous papers (see, e.g., [the first author, Methods Funct. Anal. Topol. 20, No. 4, 379–390 (2014; Zbl 1324.37039)]), the states of systems are described in terms of probability distributions and their densities. Nonlinear difference equations for the time evolution are investigated. The existence of fixed points (equilibrium states) for attractive interactions is proved under certain assumptions.

MSC:

37N40 Dynamical systems in optimization and economics
39A10 Additive difference equations
39A30 Stability theory for difference equations

Citations:

Zbl 1324.37039
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