Publication
Synchronization of two-dimensional chaotic dynamic systems by the transmission of state information
Related concepts (32)
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.
Information theory
Information theory is the mathematical study of the quantification, storage, and communication of information. The field was originally established by the works of Harry Nyquist and Ralph Hartley, in the 1920s, and Claude Shannon in the 1940s. The field, in applied mathematics, is at the intersection of probability theory, statistics, computer science, statistical mechanics, information engineering, and electrical engineering. A key measure in information theory is entropy.
Quantum information
Quantum information is the information of the state of a quantum system. It is the basic entity of study in quantum information theory, and can be manipulated using quantum information processing techniques. Quantum information refers to both the technical definition in terms of Von Neumann entropy and the general computational term. It is an interdisciplinary field that involves quantum mechanics, computer science, information theory, philosophy and cryptography among other fields.
Information
Information is an abstract concept that refers to that which has the power to inform. At the most fundamental level, information pertains to the interpretation (perhaps formally) of that which may be sensed, or their abstractions. Any natural process that is not completely random and any observable pattern in any medium can be said to convey some amount of information. Whereas digital signals and other data use discrete signs to convey information, other phenomena and artefacts such as analogue signals, poems, pictures, music or other sounds, and currents convey information in a more continuous form.
Dynamical system
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, the random motion of particles in the air, and the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured.
Dynamical systems theory
Dynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called continuous dynamical systems. From a physical point of view, continuous dynamical systems is a generalization of classical mechanics, a generalization where the equations of motion are postulated directly and are not constrained to be Euler–Lagrange equations of a least action principle.
Logistic map
The logistic map is a polynomial mapping (equivalently, recurrence relation) of degree 2, often referred to as an archetypal example of how complex, chaotic behaviour can arise from very simple nonlinear dynamical equations. The map was popularized in a 1976 paper by the biologist Robert May, in part as a discrete-time demographic model analogous to the logistic equation written down by Pierre François Verhulst. Mathematically, the logistic map is written where xn is a number between zero and one, which represents the ratio of existing population to the maximum possible population.
Hadamard's dynamical system
In physics and mathematics, the Hadamard dynamical system (also called Hadamard's billiard or the Hadamard–Gutzwiller model) is a chaotic dynamical system, a type of dynamical billiards. Introduced by Jacques Hadamard in 1898, and studied by Martin Gutzwiller in the 1980s, it is the first dynamical system to be proven chaotic. The system considers the motion of a free (frictionless) particle on the Bolza surface, i.e, a two-dimensional surface of genus two (a donut with two holes) and constant negative curvature; this is a compact Riemann surface.
Hénon map
In mathematics, the Hénon map, sometimes called Hénon–Pomeau attractor/map, is a discrete-time dynamical system. It is one of the most studied examples of dynamical systems that exhibit chaotic behavior. The Hénon map takes a point (xn, yn) in the plane and maps it to a new point The map depends on two parameters, a and b, which for the classical Hénon map have values of a = 1.4 and b = 0.3. For the classical values the Hénon map is chaotic. For other values of a and b the map may be chaotic, intermittent, or converge to a periodic orbit.
Nonlinear system
In mathematics and science, a nonlinear system (or a non-linear 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 since 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.