A hidden chaotic attractor in the classical Lorenz system
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DOI: 10.1016/j.chaos.2017.12.017
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References listed on IDEAS
- Chlouverakis, Konstantinos E. & Sprott, J.C., 2006. "Chaotic hyperjerk systems," Chaos, Solitons & Fractals, Elsevier, vol. 28(3), pages 739-746.
- Munmuangsaen, Buncha & Srisuchinwong, Banlue, 2011. "Elementary chaotic snap flows," Chaos, Solitons & Fractals, Elsevier, vol. 44(11), pages 995-1003.
- Jafari, Sajad & Sprott, J.C., 2013. "Simple chaotic flows with a line equilibrium," Chaos, Solitons & Fractals, Elsevier, vol. 57(C), pages 79-84.
- de Souza, Silvio L.T. & Batista, Antonio M. & Caldas, Iberê L. & Viana, Ricardo L. & Kapitaniak, Tomasz, 2007. "Noise-induced basin hopping in a vibro-impact system," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 758-767.
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- Algaba, A. & Fernández-Sánchez, F. & Merino, M. & Rodríguez-Luis, A.J., 2024. "Homoclinic behavior around a degenerate heteroclinic cycle in a Lorenz-like system," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
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Keywords
Nonlinear system; Chaos; Lorenz system; Self-excited attractor; Hidden attractor;All these keywords.
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