Deterministic Nonperiodic Flow

Lorenz, Edward N.

doi:10.1175/1520-0469(1963)020<0130:dnf>2.0.co;2

Cited by 15,888 publications

(4,778 citation statements)

References 8 publications

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“…Principle of chaos optimization An early proponent of chaos theory was Henri Poincaré. Chaotic systems are predictable for a while and then appear to become random [12].…”

Section: Definition Of the Repulsive Potential Fieldsupporting

confidence: 79%

An Improved Path Planning Method Based on Artificial Potential Field for a Mobile Robot

Chen

Lü

2015

Cybernetics and Information Technologies

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“…Principle of chaos optimization An early proponent of chaos theory was Henri Poincaré. Chaotic systems are predictable for a while and then appear to become random [12].…”

Section: Definition Of the Repulsive Potential Fieldsupporting

confidence: 79%

An Improved Path Planning Method Based on Artificial Potential Field for a Mobile Robot

Chen

Lü

2015

Cybernetics and Information Technologies

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“…The Lorenz equations [18] ( 3) can be transformed into a standard form (2) whose function F s is more or less complicated depending on the "measured" variable [7]. With the choice X 1 = h(x, y, z) = x L the standard function (4) is made of N d = 7 terms of which two are rational.…”

Section: B Lorenz Equationsmentioning

confidence: 99%

“…I, it is possible to extract the four different null vectors by introducing the four scaling factors κ, ν, φ and ρ in system (12) as (18) Varying these factors does not affect the dynamics from the unstable periodic orbits point of view: only the scale of the attractor is affected.…”

Section: Rössler Equationsmentioning

confidence: 99%

Discovering independent parameters in complex dynamical systems

Lainscsek

Weyhenmeyer

Sejnowski

et al. 2015

Chaos, Solitons & Fractals

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The transformation of a nonlinear dynamical system into a standard form by using one of its variables and its successive derivatives can be used to identify the relationships that may exist between the parameters of the original system such as the subset of the parameter space over which the dynamics is left invariant. We show how the size of the attractor or the time scale (the pseudo-period) can be varied without affecting the underlying dynamics. This is demonstrated for the Rössler and the Lorenz systems. We also consider the case when two Rössler systems are unidirectionally coupled and when a Lorenz system is driven by a Rössler system. In both cases, the dynamics of the coupled system is affected.

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“…The pioneering work of Lorenz [24] was made possible by numerical integration on a computer, allowing him to take nearby pairs of initial conditions and compare the trajectories. H~non [23] variety of classical and modem techniques has been exploited to find periodic orbits; their stable and unstable manifolds [20]; basins of attraction [251; fractal dimension [261; and Lyapunov exponents [17, 29, 351.…”

Section: Introductionmentioning

confidence: 99%

“…For instance, Lorenz [24] used next amplitude maps to describe some features of the dynamics; that is, he plotted z,+, against z, where z,, is the nth relative maximum of the third coordinate of the numerically calculated solution. Such maps are often useful, not only for investigating features of the Lorenz attractor [30], but also for instance in experiments on intermittency in oscillating chemical reactions [28].…”

Section: Introductionmentioning

confidence: 99%