Chaos and complexity
The subject of «Chaos» falls in a no man’s land at the edge of various disciplines; examples of «chaotic» phenomena are all around us. The essential condition for this is non-linearity; this however is not a severe limitation, since it is by far the most common property of dynamical systems. Starting from the original elementary models, the concepts were subsequently refined and developed so as to apply to more complex situations, such as the temporal evolution of meteorological phenomena, biological rhythms, population dynamics, the stability of the solar system, and even the economy. A constantly recurring theme is how to decide reliably whether an apparently erratic signal corresponds to a random process or not. Indeed, it is unwise to blindly invoke the presence of deterministic chaos even when the calculated dimension is small: concrete examples highlight the limitations inherent in any numerical assessment of the fractal dimension. Among the results is the instability of the Earth’s motion over time scales short compared to its age. Models of Earthquakes are also presented with spatiotem-poral chaotic properties quite similar to those observed in real events.Vth Blois Meetings, 1995contents: Chaos - Patterns - Complex system - Spatiotemporal Chaos - Fractals.
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