Chaos theory

By analogy, the phenomenon of insurgent ( disorganised) motion in nonlinear bodys has been assign termindinamichesky or settled topsy-turvyness. Observed disorderly appearance is non due to outer noise sources, not because of the large itemize of degrees of freedom, and not because of the dubiousness associated with quantum mechanics. It is gene appreciated by its proclaim dynamics of nonlinear deterministic system. In the word form set of the system such behavior cor acts to a distant haulage. hooking (attractor) generated to English essence attractor, in this case, the set of trajectories in phase space, which attracted any the remaining trajectories in a approximation of the attractor, also called the washstand of attraction. The term foreign is used to show the unusual properties of the attractor corresponding to disorganised behavior. Cause secondment behavior is the station of nonlinear systems exponentially breed initially close trajectories in a bou nded region of phase space. Predict the behavior of the trajectories of chaotic systems for a long age is not possible, since the predisposition to initial conditions is high, and the initial conditions, twain physical experiments and in figurer simulations, substructure be set hardly with finite precision. \n carry of topsy-turvyness. At original glance, the constitution of chaos eliminates the energy to eradicate them. In reality, the lieu is exactly the reverse gear: the instability of trajectories of chaotic systems makes them extremely nice to management. \nSuppose, for example, a system with a strange attractor, and want to translate the phase flight of steps from one institutionalise to another attractor. jumbled trajectories have the ability over clipping to fall into lyuboytochki neighborhood, be to the attractor. If you want this to observe in a time not greater than T, the in demand(p) result can be achieved by one or a serial of subtle, small breaks of the trajectory. distributively of these perturbations only slightly alter the trajectory. save after well-nigh time collection and exponential increase of small perturbations leads to a sufficiently lovesome trajectory correction. With the pay choice of perturbation it allows to solve the caper without taking forth from the trajectory of a chaotic attractor. Thus, systems with chaos demonstrate both good discourse and amazing plasticity: the system is real sensitive to external influences, while maintaining the eccentric person of motion. The combination of restraint and plasticity, according to more researchers, is the reason that the chaotic dynamics is a characteristic eccentric of behavior for many a(prenominal) vital subsystems of aliment organisms. For example, the chaotic nature of the heart rate allows the heart to respond flexibly to changes in physical and stirred stress, providing a hand over of dynamic strength.