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Chaos Communications
Chaos communications is an application of chaos theory which is aimed to provide security in the transmission of information performed through telecommunications technologies. By secure communications, one has to understand that the contents of the message transmitted are inaccessible to possible eavesdroppers. In chaos communications security (i.e., privacy) is based on the complex dynamic behaviors provided by chaotic systems. Some properties of chaotic dynamics, such as complex behaviour, noise-like dynamics ( pseudorandom noise) and spread spectrum, are used to encode data. On the other hand, chaos being a deterministic phenomenon, it is possible to decode data using this determinism. In practice, implementations of chaos communications devices resort to one of two chaotic phenomena: synchronization of chaos, or control of chaos. To implement chaos communications using such properties of chaos, two chaotic oscillators are required as a transmitter (or master) and receiver (o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chaos Theory
Chaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions, and were once thought to have completely random states of disorder and irregularities. Chaos theory states that within the apparent randomness of chaotic complex systems, there are underlying patterns, interconnection, constant feedback loops, repetition, self-similarity, fractals, and self-organization. The butterfly effect, an underlying principle of chaos, describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state (meaning that there is sensitive dependence on initial conditions). A metaphor for this behavior is that a butterfly flapping its wings in Brazil can cause a tornado in Texas. Small differences in initial conditions, such as those due to errors in measurements or due to rounding error ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Behaviour
Complex commonly refers to: * Complexity, the behaviour of a system whose components interact in multiple ways so possible interactions are difficult to describe ** Complex system, a system composed of many components which may interact with each other * Complex (psychology), a core pattern of emotions etc. in the personal unconscious organized around a common theme such as power or status Complex may also refer to: Arts, entertainment and media * Complex (English band), formed in 1968, and their 1971 album ''Complex'' * Complex (band), a Japanese rock band * ''Complex'' (album), by Montaigne, 2019, and its title track * ''Complex'' (EP), by Rifle Sport, 1985 * "Complex" (song), by Gary Numan, 1979 * Complex Networks, publisher of magazine ''Complex'', now online Biology * Protein–ligand complex, a complex of a protein bound with a ligand * Exosome complex, a multi-protein intracellular complex * Protein complex, a group of two or more associated polypeptide chains * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pseudorandom Noise
In cryptography, pseudorandom noise (PRN) is a signal similar to noise which satisfies one or more of the standard tests for statistical randomness. Although it seems to lack any definite pattern, pseudorandom noise consists of a deterministic sequence of pulses that will repeat itself after its period. In cryptographic devices, the pseudorandom noise pattern is determined by a key and the repetition period can be very long, even millions of digits. Pseudorandom noise is used in some electronic musical instruments, either by itself or as an input to subtractive synthesis, and in many white noise machines. In spread-spectrum systems, the receiver correlates a locally generated signal with the received signal. Such spread-spectrum systems require a set of one or more "codes" or "sequences" such that * Like random noise, the local sequence has a very low correlation with any other sequence in the set, or with the same sequence at a significantly different time offset, or with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spread Spectrum
In telecommunication and radio communication, spread-spectrum techniques are methods by which a signal (e.g., an electrical, electromagnetic, or acoustic signal) generated with a particular bandwidth is deliberately spread in the frequency domain, resulting in a signal with a wider bandwidth. These techniques are used for a variety of reasons, including the establishment of secure communications, increasing resistance to natural interference, noise, and jamming, to prevent detection, to limit power flux density (e.g., in satellite downlinks), and to enable multiple-access communications. Telecommunications Spread spectrum generally makes use of a sequential noise-like signal structure to spread the normally narrowband information signal over a relatively wideband (radio) band of frequencies. The receiver correlates the received signals to retrieve the original information signal. Originally there were two motivations: either to resist enemy efforts to jam the communication ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deterministic System
In mathematics, computer science and physics, a deterministic system is a system in which no randomness is involved in the development of future states of the system. A deterministic model will thus always produce the same output from a given starting condition or initial state. at Scholarpedia In physics Physical laws that are described by represent deterministic systems, even though the state of the system at a given point in time may be difficult to describe explicitly. In |
Synchronization Of Chaos
Synchronization of chaos is a phenomenon that may occur when two or more dissipative chaotic systems are coupled. Because of the exponential divergence of the nearby trajectories of chaotic systems, having two chaotic systems evolving in synchrony might appear surprising. However, synchronization of coupled or driven chaotic oscillators is a phenomenon well established experimentally and reasonably well-understood theoretically. The stability of synchronization for coupled systems can be analyzed using master stability. Synchronization of chaos is a rich phenomenon and a multi-disciplinary subject with a broad range of applications. Synchronization may present a variety of forms depending on the nature of the interacting systems and the type of coupling, and the proximity between the systems. Identical synchronization This type of synchronization is also known as complete synchronization. It can be observed for identical chaotic systems. The systems are said to be completely s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Control Of Chaos
In lab experiments that study chaos theory, approaches designed to control chaos are based on certain observed system behaviors. Any chaotic attractor contains an infinite number of unstable, periodic orbits. Chaotic dynamics, then, consists of a motion where the system state moves in the neighborhood of one of these orbits for a while, then falls close to a different unstable, periodic orbit where it remains for a limited time and so forth. This results in a complicated and unpredictable wandering over longer periods of time. Control of chaos is the stabilization, by means of small system perturbations, of one of these unstable periodic orbits. The result is to render an otherwise chaotic motion more stable and predictable, which is often an advantage. The perturbation must be tiny compared to the overall size of the attractor of the system to avoid significant modification of the system's natural dynamics. Several techniques have been devised for chaos control, but most are de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neural Cryptography
Neural cryptography is a branch of cryptography dedicated to analyzing the application of stochastic algorithms, especially artificial neural network algorithms, for use in encryption and cryptanalysis. Definition Artificial neural networks are well known for their ability to selectively explore the solution space of a given problem. This feature finds a natural niche of application in the field of cryptanalysis. At the same time, neural networks offer a new approach to attack ciphering algorithms based on the principle that any function could be reproduced by a neural network, which is a powerful proven computational tool that can be used to find the inverse-function of any cryptographic algorithm. The ideas of mutual learning, self learning, and stochastic behavior of neural networks and similar algorithms can be used for different aspects of cryptography, like public-key cryptography, solving the key distribution problem using neural network mutual synchronization, hashing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Synchronization Of Chaos
Synchronization of chaos is a phenomenon that may occur when two or more dissipative chaotic systems are coupled. Because of the exponential divergence of the nearby trajectories of chaotic systems, having two chaotic systems evolving in synchrony might appear surprising. However, synchronization of coupled or driven chaotic oscillators is a phenomenon well established experimentally and reasonably well-understood theoretically. The stability of synchronization for coupled systems can be analyzed using master stability. Synchronization of chaos is a rich phenomenon and a multi-disciplinary subject with a broad range of applications. Synchronization may present a variety of forms depending on the nature of the interacting systems and the type of coupling, and the proximity between the systems. Identical synchronization This type of synchronization is also known as complete synchronization. It can be observed for identical chaotic systems. The systems are said to be completely s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optical Communications
Optical communication, also known as optical telecommunication, is communication at a distance using light to carry information. It can be performed visually or by using electronic devices. The earliest basic forms of optical communication date back several millennia, while the earliest electrical device created to do so was the photophone, invented in 1880. An optical communication system uses a transmitter, which encodes a message into an optical signal, a channel, which carries the signal to its destination, and a receiver, which reproduces the message from the received optical signal. When electronic equipment is not employed the 'receiver' is a person visually observing and interpreting a signal, which may be either simple (such as the presence of a beacon fire) or complex (such as lights using color codes or flashed in a Morse code sequence). Modern communication relies on optical networking systems using optical fiber, optical amplifiers, lasers, switches, routers, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonlinear Systems
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists because most systems are inherently nonlinear in nature. Nonlinear dynamical systems, describing changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems. Typically, the behavior of a nonlinear system is described in mathematics by a nonlinear system of equations, which is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear as variables of a polynomial of degree higher than one or in the argument of a function which is not a polynomial of degree one. In other words, in a nonlinear system of equations, the equation(s) to be solved cannot be written as a linear combination of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
