A linear two-state model with complex dynamics |
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| Affiliation: | 1. Peter the Great St. Petersburg Polytechnic University, Department of Nuclear and Heat Power Engineering, 195251 Saint Petersburg, Russian Federation;2. Politecnico di Milano, Department of Energy, Nuclear Engineering Division, Via La Masa 34, 20156 Milan, Italy |
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| Abstract: | We study the dynamics of a stochastic two-state model in which all forces are linear. While conceptually simple, we show that the behavior of this system is surprisingly complex. The moments of the system undergo a series of bifurcations as either the overall fluctuation rate or the ratio between the two transition rates is varied. The system displays the very counterintuitive behavior in which all its spatial moments diverge in time, and yet the mean time to escape from a region that includes the origin is infinite. Finally, the system displays resonant activation in a particularly transparent way. |
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