RESUMEN
We report the first experimental observation of extreme multistability in a controlled laboratory investigation. Extreme multistability arises when infinitely many attractors coexist for the same set of system parameters. The behavior was predicted earlier on theoretical grounds, supported by numerical studies of models of two coupled identical or nearly identical systems. We construct and couple two analog circuits based on a modified coupled Rössler system and demonstrate the occurrence of extreme multistability through a controlled switching to different attractor states purely through a change in initial conditions for a fixed set of system parameters. Numerical studies of the coupled model equations are in agreement with our experimental findings.
Asunto(s)
Electrónica/instrumentación , Modelos Teóricos , Dinámicas no Lineales , Oscilometría/instrumentación , Oscilometría/métodos , Simulación por Computador , Diseño Asistido por Computadora , Diseño de Equipo , Análisis de Falla de Equipo , RetroalimentaciónRESUMEN
We propose a model of coupled random walks for stock-stock correlations. The walks in the model are coupled via a mechanism that the displacement (price change) of each walk (stock) is activated by the price gradients over some underlying network. We assume that the network has two underlying structures, describing the correlations among the stocks of the whole market and among those within individual groups, respectively, each with a coupling parameter controlling the degree of correlation. The model provides the interpretation of the features displayed in the distribution of the eigenvalues for the correlation matrix of real market on the level of time sequences. We verify that such modeling indeed gives good fitting for the market data of US stocks.
