The Rikitake system, which apparently serves as a model for the reversal of polarity of the Earth's electromagnetic field, is written:
Interestingly, I believe this predates the Lorenz attractor.
I wired up the computer to model the above; phase portraits of the Rikitake attractor for μ = 2, α = 5, x0 = 0, y0 = 0.1 and z0 = 0 are shown below (1 V/cm, scope in XY-mode), together with results from reference [1]. I've tried to adjust my results to match the scales used in [1]. Not sure why my results show a preponderance for the right hand side - I think it may be because the analog computer solution decays (over time) due to the integrators not being completely error free: by the time the solution is ready to move across to spiral around on the left hand side, errors have possibly built up, destroying the solution.
[1] Ihsan Pehlivan and Yulmaz Uyaroglu, 2007. Rikitake Attractor and its Synchronization Application for Secure Communication Systems. Journal of Applied Sciences, 7: 232-236.
Interestingly, I believe this predates the Lorenz attractor.
I wired up the computer to model the above; phase portraits of the Rikitake attractor for μ = 2, α = 5, x0 = 0, y0 = 0.1 and z0 = 0 are shown below (1 V/cm, scope in XY-mode), together with results from reference [1]. I've tried to adjust my results to match the scales used in [1]. Not sure why my results show a preponderance for the right hand side - I think it may be because the analog computer solution decays (over time) due to the integrators not being completely error free: by the time the solution is ready to move across to spiral around on the left hand side, errors have possibly built up, destroying the solution.
[1] Ihsan Pehlivan and Yulmaz Uyaroglu, 2007. Rikitake Attractor and its Synchronization Application for Secure Communication Systems. Journal of Applied Sciences, 7: 232-236.
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