chaos theory

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Related to Chaotic systems: Chaos theory

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.
References in periodicals archive ?
The multiple chaotic systems which consist of the tent chaotic map (1), the piecewise linear chaotic map (2) and the Chen's high-dimension hyper-chaotic system (3) are utilized to enlarge the key space and perform the complex dynamic behavior.
In general, the proposed ICS algorithm is a feasible, energy-efficient, and promising method for parameters estimation of chaotic systems.
Nowadays, in literature there are several approaches of implementation of chaotic systems in cryptography, because chaotic systems present cryptographic properties related to confusion and diffusion such as sensitivity to initial conditions and control parameters, mixing, determinism, and ergodicity [1, 2, 12, 13, 15].
Observed based synchronization of chaotic systems Phys Rev E 54 4803-4811.
These peculiar characteristics have led such attractors to be called strange attractors, but chaotic systems are so-called for another reason, namely that any change in the starting point of the temporal evolution of the system in the phase space, no matter how small, inflates exponentially.
Among the topics are the complexity of a kind of special shift map, positive solutions for some three-point boundary value problems, bifurcation analysis for a predator-prey system with prey refuge and diffusion, similar-short periodicity analysis and application in image compression encryption, the adaptive synchronization of the incommensurate fractional-order chaotic systems with fully unknown parameters, and applying a fractal approach to processing geochemical exploration data of the Baiyin area of Gansu Province.
In the literature, many chaotic systems have been presented [3-9,15,16], but few have been used in cryptography.
Abstract: For a robust predictability of chaotic systems, which are very sensitive to initial conditions, we propose in this paper a new approach to design a chaotic system forecaster.
The idea of synchronizing two identical chaotic systems was first introduced by Carroll and Pecora [1-2].
In 1990, pecora and carroll proposed a successful method to synchronize two identical chaotic systems with different initial conditions [1].
During last one and half decade an interesting relationship between chaos and cryptography has been developed, according to which many properties of chaotic systems such as: ergodicity, sensitivity to initial conditions/system parameters, mixing property, deterministic dynamics and structural complexity can be considered analogous to the confusion, diffusion with small change in plaintext/secret key, diffusion with a small change within one block of the plaintext, deterministic pseudo randomness and algorithmic complexity properties of traditional cryptosystems.