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The Lorenz attractor arises in the study of the Lorenz oscillator, a 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 ...
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BetaExamples of dynamical systems include population growth, a swinging pendulum, the motions of celestial bodies, and the behavior of “rational” individuals playing a negotiation game, to name a few. The first three examples sound legitimate, as those are systems that typically appear in physics textbooks. But what about the last example?
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BetaThe dynamic systems are also known as memory systems. Any continuous-time dynamic system can be described by a differential equation or any discrete-time dynamic system by a difference equation. An electric circuit containing inductors and (or) capacitors is an example of dynamic system. Also, a summer or accumulator, a delay circuit, etc. are ...
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BetaThis describes the rate of change of a quantity x with respect to time t - a simple summary of the core behavior of a dynamical system. Examples of dynamical systems theory in technology. The dynamic systems theory has found extensive use and vast application in basically every technology-based industry in the world.
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BetaContinuous dynamical systems: bifurcations Example: _x = r + x2, where r is a parameter. Figure:The phase portrait of the system _x = r + x2. Bifurcation: a qualitative change in the vector eld. J. Won, Y. Borns-Weil (MIT) Discrete and Continuous Dynamical Systems May 18, 2014 17 / 32
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BetaFigure 1: System with a single input and output signal. Static System. A system is called static if output of system is dependent on present value of input. It is also known as memory less system. Example of static systems are \[y(t) = x(t)\] \[y(t) = tx(t) + 2x(t)\]
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BetaA mixed initiative system is one whose behavior is determined by either external or internal inputs. Interestingly, in a mixed initiative system, a single external input can lead to a single state change or a sequence of changes. As an example, consider a variation of the closed Buttons and Lights World described in the preceding section.
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BetaNewton's Laws for example are incredibly accurate under known situations and formulate a well defined dynamical system. For example, problems from Classical Mechanics may be written as a dynamical system where the position and velocity of a particle or even that of a continuous medium are the state variable and Newton's Laws used as the updating rule.
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BetaIn designing control systems we must be able to model engineered system dynamics. The model of a dynamic system is a set of equations (differential equations) that represents the dynamics of the system using physics laws. The model permits to study system transients and steady state performance. Model complexity
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BetaExamples of linear time-varying systems include a car in motion or a rocket in flight, where the weight decreases as fuel is consumed. Example of a linear time-varying system: Mass of vehicle decreasing while fuel is consumed ... Dynamic systems can also be classified based on the nature of time representation: continuous-time and ...
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The Lorenz attractor arises in the study of the Lorenz oscillator, a 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 ...
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