scholarly journals Nonlinear dynamics and phase space transport by chorus emission

2021 ◽  
Vol 5 (1) ◽  
Author(s):  
Fulvio Zonca ◽  
Xin Tao ◽  
Liu Chen
Keyword(s):  
Nonlinear Dynamics ◽  
Phase Space ◽  
Phase Space Transport

Mel'nikov analysis of phase space transport in a N-degree-of-freedom Hamiltonian system

1997 ◽  
Vol 30 (3) ◽  
pp. 1365-1374 ◽  
Author(s):  
Vassilios M. Rothos ◽  
Tassos C. Bountis
Keyword(s):  
Phase Space ◽  
Hamiltonian System ◽  
Degree Of Freedom ◽  
Phase Space Transport

Properties of cross-well chaos in an impacting system

1994 ◽  
Vol 347 (1683) ◽  
pp. 391-410 ◽  
Keyword(s):  
Phase Space ◽  
Poincaré Map ◽  
Poincare Map ◽  
Chaotic Motions ◽  
Higher Harmonics ◽  
Potential Wells ◽  
Duffing's Equation ◽  
Duffing’S Equation ◽  
Phase Space Transport ◽  
Basin Boundaries

In this paper we present results on chaotic motions in a periodically forced impacting system which is analogous to the version of Duffing’s equation with negative linear stiffness. Our focus is on the prediction and manipulation of the cross-well chaos in this system. First, we develop a general method for determining parameter conditions under which homoclinic tangles exist, which is a necessary condition for cross-well chaos to occur. We then show how one may manipulate higher harmonics of the excitation in order to affect the range of excitation amplitudes over which fractal basin boundaries between the two potential wells exist. We also experimentally investigate the threshold for cross-well chaos and compare the results with the theoretical results. Second, we consider the rate at which the system crosses from one potential well to the other during a chaotic motion and relate this to the rate of phase space flux in a Poincare map defined in terms of impact parameters. Results from simulations and experiments are compared with a simple theory based on phase space transport ideas, and a predictive scheme for estimating the rate of crossings under different parameter conditions is presented. The main conclusions of the paper are the following: (1) higher harmonics can be used with some effectiveness to extend the region of deterministic basin boundaries (in terms of the amplitude of excitation) but their effect on steady-state chaos is unreliable; (2) the rate at which the system executes cross-well excursions is related in a direct manner to the rate of phase space flux of the system as measured by the area of a turnstile lobe in the Poincare map. These results indicate some of the ways in which the chaotic properties of this system, and possibly others such as Duffing’s equation, are influenced by various system and input parameters. The main tools of analysis are a special version of Melnikov’s method, adapted for this piecewise-linear system, and ideas of phase space transport.

Stochasticity in the Josephson map

1996 ◽  
Vol 56 (3) ◽  
pp. 493-506 ◽  
Author(s):  
Y. Nomura ◽  
Y. H. Ichikawa ◽  
A. T. Filipov
Keyword(s):  
Nonlinear Dynamics ◽  
Diffusion Coefficient ◽  
Phase Space ◽  
Characteristic Function ◽  
Numerical Investigation ◽  
Stochastic Diffusion ◽  
Standard Map ◽  
External Bias ◽  
Stochastic Parameter ◽  
Phase Space Portrait

The Josephson map describes the nonlinear dynamics of systems characterized by the standard map with a uniform external bias superposed. The intricate structures of the phase-space portrait of the Josephson map are examined here on the basis of the associated tangent map. A numerical investigation of stochastic diffusion in the Josephson map is compared with the renormalized diffusion coefficient calculated using the characteristic function. The global stochasticity of the Josephson map occurs at far smaller values of the stochastic parameter than is the case of the standard map.

scholarly journals Phase space transport in the interaction between shocks and plasma turbulence

2021 ◽  
Vol 118 (21) ◽  
pp. e2026764118
Author(s):  
Domenico Trotta ◽  
Francesco Valentini ◽  
David Burgess ◽  
Sergio Servidio
Keyword(s):  
Phase Space ◽  
Vlasov Equation ◽  
Coarse Graining ◽  
Plasma Turbulence ◽  
Turbulent Jet ◽  
Plasma Transport ◽  
Space Plasmas ◽  
Collisionless Shocks ◽  
Phase Space Transport

The interaction of collisionless shocks with fully developed plasma turbulence is numerically investigated. Hybrid kinetic simulations, where a turbulent jet is slammed against an oblique shock, are employed to address the role of upstream turbulence on plasma transport. A technique, using coarse graining of the Vlasov equation, is proposed, showing that the particle transport strongly depends on upstream turbulence properties, such as strength and coherency. These results might be relevant for the understanding of acceleration and heating processes in space plasmas.

scholarly journals Chaotic Saddles in a Generalized Lorenz Model of Magnetoconvection

2020 ◽  
Vol 30 (12) ◽  
pp. 2030034
Author(s):  
Francis F. Franco ◽  
Erico L. Rempel
Keyword(s):  
Nonlinear Dynamics ◽  
Fractal Dimension ◽  
Phase Space ◽  
Lyapunov Exponent ◽  
Chaotic Attractors ◽  
Maximum Lyapunov Exponent ◽  
Lorenz Model ◽  
Fractal Basin Boundaries ◽  
Chaotic Transients ◽  
Basin Boundaries

The nonlinear dynamics of a recently derived generalized Lorenz model [ Macek & Strumik, 2010 ] of magnetoconvection is studied. A bifurcation diagram is constructed as a function of the Rayleigh number where attractors and nonattracting chaotic sets coexist inside a periodic window. The nonattracting chaotic sets, also called chaotic saddles, are responsible for fractal basin boundaries with a fractal dimension near the dimension of the phase space, which causes the presence of very long chaotic transients. It is shown that the chaotic saddles can be used to infer properties of chaotic attractors outside the periodic window, such as their maximum Lyapunov exponent.

Study on the Safety Degree of Ship Capsizing in Stochastic Waves

2017 ◽  
Vol 33 (01) ◽  
pp. 24-30
Author(s):  
Jianwei Zhang ◽  
Wanqing Wu ◽  
Junquan Hu
Keyword(s):  
Phase Space ◽  
Transport Theory ◽  
Melnikov Function ◽  
Statistical Characteristics ◽  
Fast Fourier Transformation ◽  
Random Wave ◽  
Random Waves ◽  
Phase Space Transport ◽  
Heading Angle ◽  
Ship Capsizing

To quantify ship capsizing, from the energy perspective, the safety degree of a ship in waves is estimated based on stochastic Melnikov function and phase space transport theory. Considering the influence of nonlinear damping moment, nonlinear restoring moment, as well as the random waves, a nonlinear single degree of freedom differential equation for ship rolling is established. Transform the random wave moment from time domain to frequency domain by fast Fourier transformation, the random Melnikov function and rate of phase flux are extended to include the effects of navigation speed and heading angle and the safety degree of ship capsizing is quantified according to its statistical characteristics. Through an example, the accuracy of Melnikov function and phase space transport theory are verified and the effects of ship speed and heading angle on phase space transport rate are also quantified. This method is demonstrated properly to quantify the safety degree of ship capsizing and some valuable reference can be provided for the further research on ship stability criteria.

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