Universal behavior in nonlinear systems

Feigenbaum, Mitchell J.

doi:10.1016/0167-2789(83)90112-4

Cited by 442 publications

(237 citation statements)

References 8 publications

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“…Out of fluctuations ordered structures of spikes and bubbles grow continuously. The spikes increase in number, as new spikes appear in between each pair of spikes, and they thus multiply in a frequency doubling manner (Feigenbaum 1983). Later small bubbles amalgamate into larger bubbles, to form even more ordered structures (Youngs 1984).…”

Section: Hydrodynamic Stabilitymentioning

confidence: 99%

Plasma induced energy deposition and radiation transport effects in ion beam heated plane metal targets and analytic solutions of the non-linear radiation conduction equation

Long

Tahir²

1986

Laser Part. Beams

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The effects of microscopic energy deposition in hot, dense plasmas and radiation transport in plasmas, on the interaction of ion beams with plane metal targets are investigated in this paper. In order to do this we analyze the plasma dynamics of ablatively accelerated plane metal foils. The physical analysis of these results is achieved by the derivation of solutions of the non-linear radiation conduction equation with boundary temperatures which increase in time. We illustrate, by means of numerical simulations, how range shortening due to plasma effects such as increased energy loss to excited electrons and an increased effective charge due to a reduction in the recombination rate, may be compensated for by radiation transport. The effect of radiation transport and detailed microscopic energy deposition on ion beam implosions, including hydrodynamic instability, is discussed.

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Section: Hydrodynamic Stabilitymentioning

confidence: 99%

Plasma induced energy deposition and radiation transport effects in ion beam heated plane metal targets and analytic solutions of the non-linear radiation conduction equation

Long

Tahir²

1986

Laser Part. Beams

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“…The onset of the frequency comb formation is related to the loss of stability of the "original" CW state. This loss of stability proceeds via one of the standard bifurcation processes [56], such as the perioddoubling bifurcation [55]. To understand the origin of the comb formation in our system, it is therefore necessary to identify the point where nonlinearity will induce this bifurcation.…”

Section: The Origin Of Period-doubling Instabilitymentioning

confidence: 99%

“…The comb generation in a nonlinear resonator is a special example of pattern formation in nonlinear systems, and as such follows the general rules of nonlinear dynamics [55,56]. The onset of the frequency comb formation is related to the loss of stability of the "original" CW state.…”

Section: The Origin Of Period-doubling Instabilitymentioning

confidence: 99%

“…Thus, the corresponding coefficient for deviations from the CW-state has a special meaning to the stability of the cavity and, when equal to −1 (change of sign without change in deviation intensity), marks the onset of the period-doubling instability. In literature [56], such amplification coefficient is known as an eigenvalue of the monodromy matrix for perturbations, and the onset point -as the perioddoubling bifurcation point [55].…”

Section: The Origin Of Period-doubling Instabilitymentioning

confidence: 99%

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Nonlinear optics at low powers: Alternative mechanism of on-chip optical frequency comb generation

Rogov

Narimanov

2016

Phys. Rev. A

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Nonlinear optical effects provide a natural way of light manipulation and interaction, and form the foundation of applied photonics -from high-speed signal processing and telecommunication, to ultra-high bandwidth interconnects and information processing. However, relatively weak nonlinear response at optical frequencies calls for operation at high optical powers, or boosting efficiency of nonlinear parametric processes by enhancing local field intensity with high quality-factor resonators near cavity resonance, resulting in reduced operational bandwidth and increased loss due to multiphoton absorption. We present an alternative to this conventional approach, with strong nonlinear optical effects at low local intensities, based on period-doubling bifurcations near nonlinear cavity anti-resonance, and apply it to low-power optical frequency comb generation in a silicon chip.

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“…[19]. It may be thought that taking two copies of a system, relating to this universality class, and maintaining the appropriate type of coupling one can arrange the dynamical behavior characteristic to the complex analytic maps.…”

Section: Diagrams Inmentioning

confidence: 99%

Mandelbrot set in coupled logistic maps and in an electronic experiment

2001

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We suggest an approach to constructing physical systems with dynamical characteristics of the complex analytic iterative maps. The idea follows from a simple notion that the complex quadratic map by a variable change may be transformed into a set of two identical real one-dimensional quadratic maps with a particular coupling. Hence, dynamical behavior of similar nature may occur in coupled dissipative nonlinear systems, which relate to the Feigenbaum universality class. To substantiate the feasibility of this concept, we consider an electronic system, which exhibits dynamical phenomena intrinsic to complex analytic maps. Experimental results are presented, providing the Mandelbrot set in the parameter plane of this physical system. PACS number(s): 05.45.Df, 05.45.Xt

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Universal behavior in nonlinear systems

Cited by 442 publications

References 8 publications

Plasma induced energy deposition and radiation transport effects in ion beam heated plane metal targets and analytic solutions of the non-linear radiation conduction equation

Plasma induced energy deposition and radiation transport effects in ion beam heated plane metal targets and analytic solutions of the non-linear radiation conduction equation

Nonlinear optics at low powers: Alternative mechanism of on-chip optical frequency comb generation

Mandelbrot set in coupled logistic maps and in an electronic experiment

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