Trajectory Instabilities and Stochastic Behavior in Dissipative Systems with Multiple Steady States

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For a dissipative system with strong trajectory instability, a transition probability can be defined by introducing the concept of coarse graining in phase space. Computer experiments are performed on the transition probability distribution to gain a deeper insight into the macroscopic stochasticity of motion found by the author (Prog. Theor. Phys. 57 (1977), 1874) in a model system of 40 nonlinearly coupled modes. The system has several different attractors (fixed points and limit cycles). By very slight variations in the initial position, the phase point tends to different attractors via erratic trajectories. The stochasticity of these trajectories is proved definitely by showing the existence of transition probability distribution. It seems that this kind of stochastic motion arises from the very complicated overlapping of basins, unlike the case of a strange attractor. The behavior of stochastic trajectories is very sensitive to external disturbances, while the transition probability distribution is not changed appreciably by the application of random forces. Moreover, it is confirmed that the phase point fluctuating about an attractor in the presence of random forces moves to the macroscopically stochastic region after some time. No direct transition between attractors occurs. This gives rise to the phenomenon of wandering among attractors via stochastic trajectories. The phenomenon must be observed as macroscopic fluctuations. Finally, it is pointed out that similar phenomena occur also in biological and ecological systems with a multiplicity of steady states.
一般社団法人日本物理学会の論文
1979-04-01

Trajectory Instabilities and Stochastic Behavior in Dissipative Systems with Multiple Steady States

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