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... Inequality increases from about 1000 years to 2000 years and longer. When the beat period exceeds about 2000 years, chaotic behavior ensues in our integrations. This chaotic behavior is robust with respect to changes in other parameters and the initial state of the system, as well as the presence of ...
... Inequality increases from about 1000 years to 2000 years and longer. When the beat period exceeds about 2000 years, chaotic behavior ensues in our integrations. This chaotic behavior is robust with respect to changes in other parameters and the initial state of the system, as well as the presence of ...
Books
... 9. A. A. Nayfeh - Perturbation Methods, Wiley (1973); Introduction to Perturbation techniques, Wiley (1981); Problems in Perturbation, Wiley (1985). 10. J. A. Murdock - Perturbations, Theory and Methods, Wiley (1991). 11. P.B. Kahn & Y. Zarmi – Nonlinear dynamics, Wiley, New York (1998). 1 – 5: Exce ...
... 9. A. A. Nayfeh - Perturbation Methods, Wiley (1973); Introduction to Perturbation techniques, Wiley (1981); Problems in Perturbation, Wiley (1985). 10. J. A. Murdock - Perturbations, Theory and Methods, Wiley (1991). 11. P.B. Kahn & Y. Zarmi – Nonlinear dynamics, Wiley, New York (1998). 1 – 5: Exce ...
chaos - FSU High Energy Physics
... ► If you know the laws governing a body, we can predict where it will be at any given time thereafter. ► Classical physics also disregards nonlinearity. If the system behaves nonlinearly, find a linear approximation for it. ► That was the prevailing way of thinking about physics in 1960. ...
... ► If you know the laws governing a body, we can predict where it will be at any given time thereafter. ► Classical physics also disregards nonlinearity. If the system behaves nonlinearly, find a linear approximation for it. ► That was the prevailing way of thinking about physics in 1960. ...
some methods of the investigation of chaotic behaviour on
... the asymptotic behaviour must be contained in I. Fig.1. shows computer generated orbits for a large number of iterations for a discrete set of values of a, separated by narrow intervals.(Feigenbaum’s diagram). The orbit generated for fixed a approximates an asymptotic limit set. In the scale of Fig. ...
... the asymptotic behaviour must be contained in I. Fig.1. shows computer generated orbits for a large number of iterations for a discrete set of values of a, separated by narrow intervals.(Feigenbaum’s diagram). The orbit generated for fixed a approximates an asymptotic limit set. In the scale of Fig. ...
Chaos theory
Chaos theory is the field of study in mathematics that studies the behavior of dynamical systems that are highly sensitive to initial conditions—a response popularly referred to as the butterfly effect. Small differences in initial conditions (such as those due to rounding errors in numerical computation) yield widely diverging outcomes for such dynamical systems, rendering long-term prediction impossible in general. This happens even though these systems are deterministic, meaning that their future behavior is fully determined by their initial conditions, with no random elements involved. In other words, the deterministic nature of these systems does not make them predictable. This behavior is known as deterministic chaos, or simply chaos. The theory was summarized by Edward Lorenz as:Chaos: When the present determines the future, but the approximate present does not approximately determine the future.Chaotic behavior exists in many natural systems, such as weather and climate. This behavior can be studied through analysis of a chaotic mathematical model, or through analytical techniques such as recurrence plots and Poincaré maps. Chaos theory has applications in several disciplines, including meteorology, sociology, physics, engineering, economics, biology, and philosophy.