RESUMO
We report a simple model of two drive-response-type coupled chaotic oscillators, where the response system copies the nonlinearity of the driver system. It leads to a coherent motion of the trajectories of the coupled systems that establishes a constant separating distance in time between the driver and the response attractors, and their distance depends upon the initial state. The coupled system responds to external obstacles, modeled by short-duration pulses acting either on the driver or the response system, by a coherent shifting of the distance, and it is able to readjust their distance as and when necessary via mutual exchange of feedback information. We confirm these behaviors with examples of a jerk system, the paradigmatic Rössler system, a tunnel diode system and a Josephson junction-based jerk system, analytically, to an extent, and mostly numerically.
RESUMO
We show how a recently introduced statistic [Patil et al., Phys. Rev. Lett. 81, 5878 (2001)] provides a direct relationship between dimension and predictability in spatiotemporal chaotic systems. Regions of low dimension are identified as having high predictability and vice versa. This conclusion is reached by using methods from dynamical systems theory and Bayesian modeling. In this work we emphasize on the consequences for short time forecasting and examine the relevance for factor analysis. Although we concentrate on coupled map lattices and coupled nonlinear oscillators for convenience, any other spatially distributed system could be used instead, such as turbulent fluid flows.