September  2016, 36(9): 5119-5129. doi: 10.3934/dcds.2016022

A new class of 3-dimensional piecewise affine systems with homoclinic orbits

1. 

School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, China, China

Received  July 2015 Revised  December 2015 Published  May 2016

Based on mathematical analysis, this paper proves the existence of homoclinic orbits in a new class of 3-dimensional piecewise affine systems, and gives an example to illustrate the effectiveness of the method.
Citation: Tiantian Wu, Xiao-Song Yang. A new class of 3-dimensional piecewise affine systems with homoclinic orbits. Discrete & Continuous Dynamical Systems, 2016, 36 (9) : 5119-5129. doi: 10.3934/dcds.2016022
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show all references

References:
[1]

Chaos, 16 (2006), 013115, 14pp. doi: 10.1063/1.2149527.  Google Scholar

[2]

IET Image Process., 8 (2014), 33-43. doi: 10.1049/iet-ipr.2012.0586.  Google Scholar

[3]

Chaos, 20 (2010), 23107, 7pp. Google Scholar

[4]

Chaos Solitons Fract., 24 (2005), 241-255. doi: 10.1016/S0960-0779(04)00542-9.  Google Scholar

[5]

SIAM J. Appl. Dyn. Syst., 7 (2008), 1032-1048. doi: 10.1137/070709542.  Google Scholar

[6]

Chaos, 20 (2010), 013124, 8pp. doi: 10.1063/1.3339819.  Google Scholar

[7]

World Scientific, 2002. Google Scholar

[8]

Nonlinear Dyn., 69 (2012), 1915-1927. doi: 10.1007/s11071-012-0396-0.  Google Scholar

[9]

Int. J. Bifurc. Chaos, 24 (2014), 1450158, 16pp. doi: 10.1142/S0218127414501582.  Google Scholar

[10]

Electron Lett., 37 (2001), p1. doi: 10.1049/el:20010033.  Google Scholar

[11]

Chaos, 12 (2002), 344-349. Google Scholar

[12]

Physica D, 186 (2003), 133-147. doi: 10.1016/j.physd.2003.08.002.  Google Scholar

[13]

Chaos, 23 (2013), 033136, 6pp. doi: 10.1063/1.4821475.  Google Scholar

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IET Commun., 1 (2007), 1015-1022. Google Scholar

[15]

Sov. Math.Dokl., 6 (1965), 163-166. Google Scholar

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Math. USSR Sb., 10 (1970), 91-102. Google Scholar

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Part I, World Scientific, Singapore, 1998. doi: 10.1142/9789812798596.  Google Scholar

[18]

Part II, World Scientific, Singapore, 2001. doi: 10.1142/9789812798558_0001.  Google Scholar

[19]

Inst. H. Poincare Phys. Thoré., 40 (1984), 441-461.  Google Scholar

[20]

IEEE Trans. Circuits Syst., 45 (1998), 979-983. Google Scholar

[21]

$2^{nd}$ edition, Springer-Verlag, New York, 2003.  Google Scholar

[22]

Found Comput. Math., 6 (2006), 495-535. doi: 10.1007/s10208-005-0201-2.  Google Scholar

[23]

Electron. Lett., 38 (2002), 623-625. doi: 10.1049/el:20020456.  Google Scholar

[24]

Chaos Solitons Fract., 18 (2003), 25-29. doi: 10.1016/S0960-0779(02)00638-0.  Google Scholar

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