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A distinguishing feature of systems studied by chaos theory is that unstable aperiodic behaviour can be found in mathematically simple systems. Very simple, rigorously defined mathematical models can display behaviour that is awesomely complex. Another distinguishing characteristic of chaotic systems is their sensitive dependence on initial conditions – infinitesimally small changes at the start lead to bigger changes later. This behaviour is described as the signature of chaos.
The Fractal Geometry of Nature
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What is strange about strange attractors? First: they look strange. A multi-dimensional imaginary object is bound to look strange. Second: the motion on the strange attractors has sensitive dependence on initial conditions. Third: strange attractors reconcile contradictory effects: (a) they are attractors, which means that nearby trajectories converge on them; and (b) they exhibit sensitive dependence on initial conditions, which means that trajectories initially close together on the attractors diverge rapidly. Fourth: and this is the tricky bit – while strange attractors exist in an infinite
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The process of self-organization happens spontaneously – as though by magic! Think of a flock of birds taking off to fly to their place of migration. They adjust and adapt to their neighbours and unconsciously organize themselves into a patterned flock.
The edge of chaos
A series of warm winters and hot summers may simply mean that the system is revolving around one part of the phase space. It does not necessarily mean that long-term permanent change has set in.
About greenhouse effect
In the relevant sciences, the style of discourse can no longer be demonstration, as from empirical data to true conclusions. Rather, it must be dialogue, recognizing uncertainty value-commitments, and a plurality of legitimate perspectives. These are the basis for post-normal science.
After addition of chaos theory to science
chaos is not a discipline in its own right. Rather, it’s just a subcomponent of nonlinear dynamics which is itself just part of complex systems.
