<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In term of the global random attractors theory, global dynamics of nonlinear stochastic heat conduction driven by multiplicative white noise with a variable coefficient are investigated numerically. It is shown that global 𝒟-bifurcation, secondary global 𝒟-bifurcation and complex dynamical behavior occur in motion of the system with increasing the intensity of linear component in the heat source. Furthermore, the results obtained here indicate that Hasudorff dimension which is relevant to global Lyapunov exponent can be used to describe global dynamics of the associated system qualitatively.</p></abstract>

In term of the global random attractors theory, global dynamics of nonlinear stochastic heat conduction driven by multiplicative white noise with a variable coefficient are investigated numerically. It is shown that global 𝒟-bifurcation, secondary global 𝒟-bifurcation and complex dynamical behavior occur in motion of the system with increasing the intensity of linear component in the heat source. Furthermore, the results obtained here indicate that Hasudorff dimension which is relevant to global Lyapunov exponent can be used to describe global dynamics of the associated system qualitatively.

Numerical investigation on global dynamics for nonlinear stochastic heat conduction via global random attractors theory

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

In term of the global random attractors theory, global dynamics of nonlinear stochastic heat conduction driven by multiplicative white noise with a variable...

	Case I	Case II	Case III	Case IV
α	1	2.4	4	6

Hausdorff dimenison	0	1	2	3

Numerical investigation on global dynamics for nonlinear stochastic heat conduction via global random attractors theory

Published Online: Oct 03, 2018

Page range: 175 - 186

Received: Mar 09, 2018

Accepted: May 17, 2018

DOI: https://doi.org/10.21042/AMNS.2018.1.00014

Keywords
nonlinear stochastic heat conduction, global dynamics, random invariant measure, Hausdorff dimension, global Lyapunov exponent

© 2018 H. Chen et al., published by Sciendo.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Fig. 1

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Fig. 11

The values of α and corresponding Hasudorff dimension

The one to for order eigenvalues for A

Numerical investigation on global dynamics for nonlinear stochastic heat conduction via global random attractors theory

Published Online: Oct 03, 2018

Page range: 175 - 186

Received: Mar 09, 2018

Accepted: May 17, 2018

DOI: https://doi.org/10.21042/AMNS.2018.1.00014

Keywordsnonlinear stochastic heat conduction, global dynamics, random invariant measure, Hausdorff dimension, global Lyapunov exponent

© 2018 H. Chen et al., published by Sciendo.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Fig. 9

Fig. 10

Fig. 11

The values of α and corresponding Hasudorff dimension

The one to for order eigenvalues for A

Keywords
nonlinear stochastic heat conduction, global dynamics, random invariant measure, Hausdorff dimension, global Lyapunov exponent