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New derived systems of Hide's coupled dynamo model

Journal Name:

  • European Journal of Pure and Applied Mathematics

Publication Year:

  • 2017

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Abstract (2. Language): 
In this paper, we present the results of a preliminary analytical and numerical study of new derived system of single and double coupled self-exciting Faraday disk homopolar dynamos by Hide et al [3, 7]. Also, well-known systems including, Rikitake and Bullard systems have been reached by using Tikhonov theorem [6, 10] and eliminating method.
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REFERENCES

References: 

[1] A.E. Cook and P.H. Roberts. The rikitake two-disc dynamo system. Proc. Cambridge Philos Soc., 68:547, 1970.
[2] Bullard E.C. The stability of a homopolar dynamo. Proc. Cambridge Philos Soc.,
51:744-760, 1955.
[3] Skeldon A. C. Hide R. and Acheson D. A study of two novel self-exciting single-disk homopolar dynamos: theory. Proc. R. Soc. Lond, pages 1369-1395, 1996.
[4] Andrew M. Soward Irene M. Moroz, Raymond Hide. On self-exciting coupled faraday disk homopolar dynamos driving series motors. Physica D, 117:128-144, 1998.
[5] Guckenheimer J. and P. Holmes. Nonlinear Oscillations, Dynamical Sytems and Bifurcations of Vector Fields. Springer-Verlag, 1998.
[6] Wlodzimierz Klonowski. Simplifying principles for chemical and enzyme reaction kinetics. Biophysical Chemistry, 18(2):73-87, 1983.
[7] Hide R. The nonlinear differential equations governing a hierarchy of self-exciting coupled faraday-disk homopolar dynamos. Phys. Earth Plant. Int., 103:281-291, 1997.
[8] P. Swinnton-Dyer and T. Wegenknecht. Some third order ordinary differential equa¬tions. Bull London Math Soc, 40(5):725-748, 2008.
[9] Rikitake T. Oscillations of a system of disk dynamos. Proc. Cambridge Philos Soc.,
54:89-105, 1958.
[10] A. N. Tikhonov. Systems of differential equations containing small parameters in the derivatives. Mat. Sb. (N.S.), 31(73)(3):575-586, 1952.

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