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Pure Mathematics 2020
一类超混沌的Faraday圆盘发电机的Zero-Zero-Hopf分支
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Abstract:
| [1] | Hide, R., Skeldon, A.C. and Acheson, D.J. (1996) A Study of Two Novel Self-Exciting Single-Disk Homopolar Dy-namos: Theory. Proceedings of the Royal Society of London. Series A, 452, 1369-1395. https://doi.org/10.1098/rspa.1996.0070 |
| [2] | Hide, R. (1997) Nonlinear Quenching of Current Fluctuations in a Self-Exciting Homopolar Dynamo. Nonlinear Processes in Geophysics, 4, 201-205. https://doi.org/10.5194/npg-4-201-1997 |
| [3] | Hide, R. (1997) The Nonlinear Differential Equations Governing a Hierarchy of Self-Exciting Coupled Faraday-Disk Homopolar Dynamos. Physics of the Earth and Planetary Interiors, 103, 281-291. https://doi.org/10.1016/S0031-9201(97)00038-1 |
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| [5] | Moroz, I.M., Hide, R. and Soward, A.M. (1998) On Self-Exciting Coupled Faraday Disk Homopolar Dynamos Driving Series Motors. Physica D, 117, 128-144. https://doi.org/10.1016/S0167-2789(97)00305-9 |
| [6] | Moroz, I.M. (2001) On the Behavior of a Self-Exciting Faraday Disk Homopolar Dynamo with Battery in the Presence of an External Magnetic Field. International Journal of Bifurcation and Chaos, 11, 1695-1705. https://doi.org/10.1142/S0218127401002948 |
| [7] | Moroz, I.M. (2001) Self-Exciting Faraday Disk Homopolar Dynamos. International Journal of Bifurcation and Chaos, 11, 2961-2975. https://doi.org/10.1142/S0218127401004017 |
| [8] | Moroz, I.M. (2002) On the Behavior of a Self-Exciting Faraday Disk Homopolar Dynamo with a Variable Nonlinear Series Motor. International Journal of Bifurcation and Chaos, 12, 2123-2135. https://doi.org/10.1142/S0218127402005728 |
| [9] | Moroz, I.M. (2005) The Extended Malkus-Robbins Dynamo as a Perturbed Lorenz System. Nonlinear Dynamics, 41, 191-210. https://doi.org/10.1007/s11071-005-2808-x |
| [10] | Hide, R. and Moroz, I.M. (1999) Effects Due to Induced Azi-muthal Eddy Currents in a Self-Exciting Faraday Disk Homopolar Dynamo with a Nonlinear Series Motor. I.: Two Special Cases. Physica D, 134, 287-301. https://doi.org/10.1016/S0167-2789(99)00107-4 |
| [11] | Moroz, I.M. (2011) Unstable Periodic Orbits in a Four-Dimensional Faraday Disk Dynamo. Geophysical & Astrophysical Fluid Dynamics, 105, 273-286. https://doi.org/10.1080/03091929.2010.511206 |
| [12] | Llibre, J. and Makhlouf, A. (2016) Zero-Hopf Bifurcation in the Generalized Michelson System. Chaos Solitons & Fractals, 89, 228-231. https://doi.org/10.1016/j.chaos.2015.11.013 |
| [13] | Euzebio, R.D. and Llibre, J. (2017) Zero-Hopf Bifurcation in a Chua System. Nonlinear Analysis: Real World Applications, 37, 31-40. https://doi.org/10.1016/j.nonrwa.2017.02.002 |
| [14] | Candido, M.R. and Llibre, J. (2018) Zero-Hopf Bifurcations in 3-Dimensional Differential Systems with No Equilibria. Mathematics and Computers in Simulation, 151, 54-76. https://doi.org/10.1016/j.matcom.2018.03.008 |
| [15] | Cid-Montiel, L., Llibre, J. and Stoica, C. (2014) Zero-Hopf Bifurcation in a Hyperchaotic Lorenz System. Nonlinear Dynamics, 75, 561-566. https://doi.org/10.1007/s11071-013-1085-3 |
| [16] | Chen, Y.M. and Liang, H.H. (2017) Zero-Zero-Hopf Bifurcation and Ultimate Bound Estimation of a Generalized Lorenz-Stenflo Hyperchaotic System. Mathematical Methods in the Applied Sciences, 40, 3424-3432. https://doi.org/10.1002/mma.4236 |
