STRANGE ATTRACTORS IN A PERIODICALLY PERTURBED LORENZ-LIKE EQUATION

Fengjuan Chen; Liqun Zhou

doi:10.11948/2013010

2013 Volume 3 Issue 2

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Fengjuan Chen, Liqun Zhou. STRANGE ATTRACTORS IN A PERIODICALLY PERTURBED LORENZ-LIKE EQUATION[J]. Journal of Applied Analysis & Computation, 2013, 3(2): 123-132. doi: 10.11948/2013010

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Fengjuan Chen, Liqun Zhou. STRANGE ATTRACTORS IN A PERIODICALLY PERTURBED LORENZ-LIKE EQUATION[J]. Journal of Applied Analysis & Computation, 2013, 3(2): 123-132. doi: 10.11948/2013010

STRANGE ATTRACTORS IN A PERIODICALLY PERTURBED LORENZ-LIKE EQUATION

College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, China

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Abstract

Abstract

This paper studies a periodically perturbed Lorenz-like equation. We obtain three types of attractors:(i) periodic sinks, (ii) Hénon-like attractors, and (iii) rank one attractors. Among the three, (i) represent the stable dynamics of equation, and (ii) and (iii) represent chaotic behaviors characterized by an Sinai-Ruelle-Bowen(SRB) measure. Each attractor admits an basin of positive Lebesgue measure, hence we observe it in numerical simulations.
- Homoclinic tangle /
- Hénon-like attractor /
- rank one attractor /
- SRB measure
MSC: 37D45;37C40

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References

[1]	A. Arneodo, P. Coullet and C. Tresser, A possible new mechnism for the onset of turbulence, Physics Letters A 81(1981),197-201. Google Scholar
[2]	M. Benedicks and L.-S. Young, Sinai-Bowen-Ruelle measure for certain Hénon maps, Invent.Math. 112(1993),541-576. Google Scholar
[3]	V. Carbone, G. Cipparrone and G. Russo, Homoclinic gluing bifurcations during the light induced reorientation in nematic-liquid-crystal films, Phys.Rev.E. 63(2001),051701. Google Scholar
[4]	F.J. Chen, A.Oksasoglu and Q.D. Wang, Heteroclinic tangles in time-periodic equations, J.Differ.Equ. 254(2013),1137-1171. Google Scholar
[5]	Q.D. Wang and A. Oksasoglu, Dynamics of homoclinic tangles in periodically perturbed second-order equations, J.Differential Equations, 250(2011),710-751. Google Scholar
[6]	Q.D. Wang and A. Oksasoglu, Periodic occurrence of chaotic behavior of homoclinic tangles, Physica D:Nonlinear Phenomena 239(2010),387-395. Google Scholar
[7]	Q.D. Wang, Periodically forced double homoclinic loops to a dissipative saddle, Preprint. Google Scholar
[8]	L.-S. Young,What are SRB measures, and which dynamical systems have them? J.Stat.Phys. 108(2002),733-754. Google Scholar