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Artin billiard

In mathematics and physics, the Artin billiard is a type of a dynamical billiard first studied by Emil Artin in 1924. It describes the geodesic motion of a free particle on the non-compact Riemann sur

Hyperion (moon)

Hyperion /haɪˈpɪəriən/, also known as Saturn VII, is a moon of Saturn discovered by William Cranch Bond, his son George Phillips Bond and William Lassell in 1848. It is distinguished by its irregular

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 non-li

Tent map

In mathematics, the tent map with parameter μ is the real-valued function fμ defined by the name being due to the tent-like shape of the graph of fμ. For the values of the parameter μ within 0 and 2,

Double pendulum

In physics and mathematics, in the area of dynamical systems, a double pendulum also known as a chaos pendulum is a pendulum with another pendulum attached to its end, forming a simple physical system

Hénon map

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 ma

Chialvo map

The Chialvo map is a two-dimensional map proposed by Dante R. Chialvo in 1995 to describe the generic dynamics of excitable systems. The model is inspired by Kunihiko Kaneko's Coupled map lattice (CML

Competitive Lotka–Volterra equations

The competitive Lotka–Volterra equations are a simple model of the population dynamics of species competing for some common resource. They can be further generalised to the Generalized Lotka–Volterra

Bogdanov map

In dynamical systems theory, the Bogdanov map is a chaotic 2D map related to the Bogdanov–Takens bifurcation. It is given by the transformation: The Bogdanov map is named after Rifkat Bogdanov.

Horseshoe map

In the mathematics of chaos theory, a horseshoe map is any member of a class of chaotic maps of the square into itself. It is a core example in the study of dynamical systems. The map was introduced b

Interval exchange transformation

In mathematics, an interval exchange transformation is a kind of dynamical system that generalises circle rotation. The phase space consists of the unit interval, and the transformation acts by cuttin

Tinkerbell map

The Tinkerbell map is a discrete-time dynamical system given by: Some commonly used values of a, b, c, and d are
*
* Like all chaotic maps, the Tinkerbell Map has also been shown to have periods; af

List of chaotic maps

In mathematics, a chaotic map is a map (namely, an evolution function) that exhibits some sort of chaotic behavior. Maps may be parameterized by a discrete-time or a continuous-time parameter. Discret

Rabinovich–Fabrikant equations

The Rabinovich–Fabrikant equations are a set of three coupled ordinary differential equations exhibiting chaotic behaviour for certain values of the parameters. They are named after Mikhail Rabinovich

Complex squaring map

In mathematics, the complex squaring map, a polynomial mapping of degree two, is a simple and accessible demonstration of chaos in dynamical systems. It can be constructed by performing the following

Brusselator

The Brusselator is a theoretical model for a type of autocatalytic reaction.The Brusselator model was proposed by Ilya Prigogine and his collaborators at the Université Libre de Bruxelles. It is a por

Mackey–Glass equations

In mathematics and mathematical biology, the Mackey–Glass equations, named after Michael Mackey and Leon Glass, refer to a family of delay differential equations whose behaviour manages to mimic both

Rössler attractor

The Rössler attractor /ˈrɒslər/ is the attractor for the Rössler system, a system of three non-linear ordinary differential equations originally studied by Otto Rössler in the 1970s. These differentia

Elastic pendulum

In physics and mathematics, in the area of dynamical systems, an elastic pendulum (also called spring pendulum or swinging spring) is a physical system where a piece of mass is connected to a spring s

Chua's circuit

Chua's circuit (also known as a Chua circuit) is a simple electronic circuit that exhibits classic chaotic behavior. This means roughly that it is a "nonperiodic oscillator"; it produces an oscillatin

Kuramoto–Sivashinsky equation

In mathematics, the Kuramoto–Sivashinsky equation (also called the KS equation or flame equation) is a fourth-order nonlinear partial differential equation. It is named after Yoshiki Kuramoto and Greg

Ikeda map

In physics and mathematics, the Ikeda map is a discrete-time dynamical system given by the complex map The original map was proposed first by as a model of light going around across a nonlinear optica

Lorenz 96 model

The Lorenz 96 model is a dynamical system formulated by Edward Lorenz in 1996. It is defined as follows. For : where it is assumed that and and . Here is the state of the system and is a forcing const

Colpitts oscillator

A Colpitts oscillator, invented in 1918 by American engineer Edwin H. Colpitts, is one of a number of designs for LC oscillators, electronic oscillators that use a combination of inductors (L) and cap

Mixmaster universe

The Mixmaster universe (named after Sunbeam Mixmaster, a brand of Sunbeam Products electric kitchen mixer) is a solution to Einstein field equations of general relativity studied by Charles Misner in

Baker's map

In dynamical systems theory, the baker's map is a chaotic map from the unit square into itself. It is named after a kneading operation that bakers apply to dough: the dough is cut in half, and the two

Three-body problem

In physics and classical mechanics, the three-body problem is the problem of taking the initial positions and velocities (or momenta) of three point masses and solving for their subsequent motion acco

Dyadic transformation

The dyadic transformation (also known as the dyadic map, bit shift map, 2x mod 1 map, Bernoulli map, doubling map or sawtooth map) is the mapping (i.e., recurrence relation) (where is the set of seque

Kicked rotator

The kicked rotator, also spelled as kicked rotor, is a paradigmatic model for both Hamiltonian chaos (the study of chaos in Hamiltonian systems) and quantum chaos. It describes a free rotating stick (

Kaplan–Yorke map

The Kaplan–Yorke map is a discrete-time dynamical system. It is an example of a dynamical system that exhibits chaotic behavior. The Kaplan–Yorke map takes a point (xn, yn ) in the plane and maps it t

Lorenz system

The Lorenz system is a system of ordinary differential equations first studied by mathematician and meteorologist Edward Lorenz. It is notable for having chaotic solutions for certain parameter values

Duffing map

The Duffing map (also called as 'Holmes map') is a discrete-time dynamical system. It is an example of a dynamical system that exhibits chaotic behavior. The Duffing map takes a point (xn, yn) in the

Van der Pol oscillator

In dynamics, the Van der Pol oscillator is a non-conservative oscillator with non-linear damping. It evolves in time according to the second-order differential equation: where x is the position coordi

Thomas' cyclically symmetric attractor

In the dynamical systems theory, Thomas' cyclically symmetric attractor is a 3D strange attractor originally proposed by René Thomas. It has a simple form which is cyclically symmetric in the x,y, and

Coupled map lattice

A coupled map lattice (CML) is a dynamical system that models the behavior of non-linear systems (especially partial differential equations). They are predominantly used to qualitatively study the cha

Arnold's cat map

In mathematics, Arnold's cat map is a chaotic map from the torus into itself, named after Vladimir Arnold, who demonstrated its effects in the 1960s using an image of a cat, hence the name. Thinking o

Bak–Sneppen model

The Bak–Sneppen model is a simple model of co-evolution between interacting species. It was developed to show how self-organized criticality may explain key features of the fossil record, such as the

Standard map

The standard map (also known as the Chirikov–Taylor map or as the Chirikov standard map) is an area-preserving chaotic map from a square with side onto itself. It is constructed by a Poincaré's surfac

Arnold tongue

In mathematics, particularly in dynamical systems, Arnold tongues (named after Vladimir Arnold) are a pictorial phenomenon that occur when visualizing how the rotation number of a dynamical system, or

Chirikov criterion

The Chirikov criterion or Chirikov resonance-overlap criterionwas established by the Russian physicist Boris Chirikov.Back in 1959, he published a seminal article,where he introduced the very first ph

Hindmarsh–Rose model

The Hindmarsh–Rose model of neuronal activity is aimed to study the spiking-bursting behavior of the membrane potential observed in experiments made with a single neuron. The relevant variable is the

Duffing equation

The Duffing equation (or Duffing oscillator), named after (1861–1944), is a non-linear second-order differential equation used to model certain damped and driven oscillators. The equation is given by

Gingerbreadman map

In dynamical systems theory, the Gingerbreadman map is a chaotic two-dimensional map. It is given by the piecewise linear transformation:

Zaslavskii map

The Zaslavskii map is a discrete-time dynamical system introduced by George M. Zaslavsky. It is an example of a dynamical system that exhibits chaotic behavior. The Zaslavskii map takes a point in the

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

Hénon–Heiles system

While at Princeton in 1962, Michel Hénon and Carl Heiles worked on the non-linear motion of a star around a galactic center with the motion restricted to a plane. In 1964 they published an article tit

Exponential map (discrete dynamical systems)

In the theory of dynamical systems, the exponential map can be used as the evolution function of the discrete nonlinear dynamical system.

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