9 thoughts

1. The crutial for the existence of chaos in a system is number of degrees of freedom and number of conservation laws. If the number of degrees of freedom is larger than the number of conservation.

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2. Mathematical Software - Chaotic Systems - Tutorial Chaotic Systems - Introduction Chaotic Systems - Definitions. A criterion of chaotic behavior of the system in time is exponential instability of phase trajectories and a fractal dimension of its attractor. The latter means that a chaotic attractor demontrates a geometric complexity.

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3. Main Theorem. Consider the drive chaotic system (1) satisfying the assumptions A1 and A2. The observer-based driven system (2) associated the proposed control law (7) and the adaptation algorithm (8) globally asymptotically synchronizes the drive system, i.e. ke–tƒk‹kx–tƒÿ^x–tƒk!0 as t .

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4. 2. The new chaotic system and its basic properties. In retrospect, Chen found a new system based on some chaotification analysis, and a linear feedback control term u =-ax + (c + 1) y was added to the second equation of the Lorenz system.

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5. This chapter introduces chaotic behaviour by examining three systems — an electronic circuit, an iterated map model (the logistic map), and a set of differential equations (the Lorenz model) — and their behaviour in state space (phase space). Bifurcations are introduced as changes in dynamical behaviour as parameters describing the systems are changed.

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6. Chaos theory is a branch of mathematics focusing on the study of chaos—states of dynamical systems whose apparently-random states of disorder and irregularities are often governed by deterministic laws that are highly sensitive to initial conditions. Chaos theory is an interdisciplinary theory stating that, within the apparent randomness of chaotic complex systems, there are underlying.

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7. There are exceptions to the chaotic storage system, including items that need to be refrigerated, kept at different humidities, or are bulky slow-sellers that can’t be stored normally. There is also room for error, such as when the computer system goes down and no items can be located. However, the possibility for a computer crash pales in Missing: Exploration.

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8. The behavior of a chaotic system is a collection of many orderly behaviors, none of which dominates under ordinary circumstances by perturbing a chaotic system in the right way, [it] can be encouraged to follow one of its many regular behaviors. In this article, Ditto and Pecora also point out that a chaotic signal can drive stable parts.

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9. In this paper, we are interested in searching a link between the 3D and 4D system through which it designs a hyper-chaotic system 4D. We have constructed new hyper-chaotic systems by adding another state variable in the chaotic dynamical systems to the three dimensions which were developed by Lorenz [1], Lü [2] and Rossler [3].

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