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.
PRaCto: Pseudo Random bit generator for Cryptographic application
In this work, the random variable r where in equation (3) was substituted by the chaotic system function as shown in equation (10).
Continuous Time Chaotic Systems for Whale Optimization Algorithm
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.
Synchronization of Different Uncertain Fractional-Order Chaotic Systems with External Disturbances via T-S Fuzzy Model
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.
On the Q-S Chaos Synchronization of Fractional-Order Discrete-Time Systems: General Method and Examples
Hoang, "A chaotic system with rounded square equilibrium and with no-equilibrium," Optik - International Journal for Light and Electron Optics, vol.
Autonomous Jerk Oscillator with Cosine Hyperbolic Nonlinearity: Analysis, FPGA Implementation, and Synchronization
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.
Circuit Implementation, Synchronization of Multistability, and Image Encryption of a Four-Wing Memristive Chaotic System
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.
Image Encryption Algorithm Based on Hyperchaotic Maps and Nucleotide Sequences Database
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.
Characteristic Analysis of Fractional-Order 4D Hyperchaotic Memristive Circuit
Properties of the 4D Memristor No Equilibrium Chaotic System
Fractional Order Memristor No Equilibrium Chaotic System with Its Adaptive Sliding Mode Synchronization and Genetically Optimized Fractional Order PID Synchronization
Gong, "Synchronization of the fractional-order chaotic system via adaptive observer," Systems Science & Control Engineering, vol.
Bifurcation Analysis and Chaos Control of a Fractional Order Portal Frame with Nonideal Loading Using Adaptive Sliding Mode Control
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.
STABILIZATION OF CHAOS RIKITAKE SYSTEM BY USE OF FUZZY CONTROLLER
How long will it take for us to accept that global temperatures, like the weather, is a chaotic system?
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