By Gregoire Nicolis
Complexity is rising as a post-Newtonian paradigm for drawing close a wide physique of phenomena of shock on the crossroads of actual, engineering, environmental, existence and human sciences from a unifying viewpoint. This ebook outlines the principles of contemporary complexity learn because it arose from the cross-fertilization of rules and instruments from nonlinear technology, statistical physics and numerical simulation. it really is proven how those advancements bring about an figuring out, either qualitative and quantitative, of the complicated structures encountered in nature and in daily event and, conversely, how typical complexity acts as a resource of idea for development on the basic point.
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Example text
But in a power law the same transformation keeps the exponent H invariant, producing merely a multiplicative factor. We express this by qualifying this law as scale invariant. The distinction breaks down for nonlinear transformations, for which a power law can become exponential and vice versa. As we see later deterministic chaos can be associated with variabilities of either of the two kinds, depending on the mechanisms presiding in its generation. 3 Collective problem solving: food recruitment in ants In the preceding examples the elements constituting the system of interest were the traditional ones considered in physical sciences: molecules, volume elements in a fluid or in a chemical reagent, and so forth.
Once on such a point the system will no longer evolve. Point attractors, also referred as fixed points, are therefore models of steady-state solutions of the evolution equations. 2) and of the geometry of the phase space portrait is stability, to which we referred already in qualitative terms in Sec. 3. Let γs be a “reference” phase trajectory describing a particular long-time behavior of the system at hand. g. a fixed point. 3) the trajectory that will in fact be realized will be a displaced one, γ whose instantaneous displacement from γs we denote by δxt (Fig.
An example of this description is provided by the equations of population dynamics. 6) and the like, these equations are to be seen as models, established empirically or proposed ad hoc to be verified at a later stage by experiment. ). This point is taken up further in Sec. 7. 3 Thermodynamic formulation The advantage of disposing of a description like the macroscopic description, limited to a small set of key variables, is gained at the considerable expense that the universality of the microscopic description is here lost.