# chaos theory

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## chaos theory

a branch of mathematics that seeks to predict widespread effects of small (or minute) and possibly remote triggering events; the unpredictable course of some epidemics and malignant metastases may accord with chaos theory.

## chaos theory

The mathematical conception that some phenomena that seem random may be of a deterministic order highly sensitive to initial conditions and perturbations. There is a growing appreciation that chaos may be a feature of many biological systems and that chaos theory may prove to have many applications in medicine.
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Chaotic systems have properties like ergodicity, sensitivity to initial condition, mixing property, and also have deterministic dynamic and complex structure.
In this work, the random variable r where in equation (3) was substituted by the chaotic system function as shown in equation (10).
In this section, in order to further illustrate the effectiveness of the proposed control method designed in previous sections, one example about the synchronization for two different uncertain fractional-order chaotic system is given.
In this paper, we are concerned with the Q-S synchronization of fractional-order discrete-time chaotic systems with different dimensions and non-identical orders.
Hoang, "A chaotic system with rounded square equilibrium and with no-equilibrium," Optik - International Journal for Light and Electron Optics, vol.
It can be seen that the Lyapunov dimension is fractional which means it is chaotic system. The phase diagrams listed in Figure 1 show that the chaotic attractor trajectory has ergodicity and boundedness in a specific attraction domain.
Compared with low-dimensional chaotic systems, high-dimensional chaotic systems have more positive Lyapunov exponents and are more complex, thus making it difficult to predict the dynamic characteristics that can effectively solve the degradation problem of low-dimensional chaotic system dynamics characteristics.
It is mainly because of the differences defined by the SE and [C.sub.0] definitions, which mean that complexity can also reflect the dynamic characteristics of a chaotic system.
Gong, "Synchronization of the fractional-order chaotic system via adaptive observer," Systems Science & Control Engineering, vol.
In the next section will apply control signal on chaotic system and while will assume the initial conditions and will monitor the effect of our controller on this chaotic system.
How long will it take for us to accept that global temperatures, like the weather, is a chaotic system?

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