Nonlinear systems

thumb|right|Electric displacement field of a ferroelectric material as the [[electric field is first decreased, then increased. The curves form a hysteresis loop.]] Hysteresis is the dependence of the state of a system on its history. For example, a magnet may have more than one possible magnetic moment in a given magnetic field, depending on how the field changed in the past. Such a system is called hysteretic. Plots of a single component of the moment often form a loop or hysteresis curve, where there are different values of one variable depending on the direction of change of another variab

system in which the change of the output is not proportional to the change of the input

System of ordinary differential equations first studied by Edward Lorenz

area of mathematics

mathematical model describing how action potentials in neurons are initiated and propagated

closed trajectory in a 2d phase space of a dynamical system such that that another trajectory spirals into it as time approaches ±∞

exactly solvable model of coupled oscillators

thumb|300px|Schematic representation of a self-oscillation as a positive feedback loop. The oscillator V produces a feedback signal B. The controller at R uses this signal to modulate the external power S that acts on the oscillator. If the power is modulated in phase with the oscillator's velocity, a negative damping is established and the oscillation grows until limited by nonlinearities.

describes a prototype of an excitable system (e.g., a neuron)

non-linear second order differential equation and its attractor

branch of physics and acoustics

apparent paradox in chaos theory that many complicated enough physical systems exhibited almost exactly periodic behavior instead of ergodic behavior

Event in dynamical systems theory

In mathematical analysis, a '''C0-semigroup, also known as a strongly continuous one-parameter semigroup''', is a generalization of the exponential function. Just as exponential functions provide solutions of scalar linear constant coefficient ordinary differential equations, strongly continuous semigroups provide solutions of linear constant coefficient ordinary differential equations in Banach spaces. Such differential equations in Banach spaces arise from e.g. delay differential equations and partial differential equations.

Conceptual framework

cellular automaton

Autowaves are self-supporting non-linear waves in active media (i.e. those that provide distributed energy sources). The term is generally used in processes where the waves carry relatively low energy, which is necessary for synchronization or switching the active medium.