MULTISPIRAL Strange Attractors in a Quasi-Periodically forced system

See my paper :

Ref ,

in the Int. Journ. of Bifurcation and Chaos 9(6), 1009-1039, (1999), (IJBC).

*See also a Gallery of multispiral Strange Attractors in the modified Chua's dynamical system

*See also some multispiral Strange Attractors in some nonautonomous dynamical system

*See also some multispiral Strange Attractors in some Brocket type system

*See also some multi-buckle Strange Attractors in some Van der pol type system

Kapitaniak [1997] studied the following quasi-periodically forced system which was first proposed by Reich [1961]:

{dx}/{dt} = y-f_2(x), {dy}/{dt} = -beta[x+(v+1)y)+A(sin(omega_1 . t) + sin(\omega_2 . t)],

where x and y are functions of t, f_2 is the Chua's nonlinearity and, beta, A, v, omega_1 and omega_2 are the parameters of the system. In the ref. given above, I modified f_2 to get some new multispiral strange attractors:

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left-1-spiral strange attractor exhibited by the modified Reich-Kapitaniak's system

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right-1-spiral strange attractor exhibited by the modified Reich-Kapitaniak's system

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Combination of these previous attractors with the formation of a double-one-spiral chaotic attractor.

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left-2-spiral strange attractor exhibited by the modified Reich-Kapitaniak's system

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right-2-spiral strange attractor exhibited by the modified Reich-Kapitaniak's system

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Combination of these previous attractors with the formation of a double-two-spiral chaotic attractor.

[IMAGE]

left-3-spiral strange attractor exhibited by the modified Reich-Kapitaniak's system

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right-3-spiral strange attractor exhibited by the modified Reich-Kapitaniak's system

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Combination of these previous attractors with the formation of a double-three-spiral chaotic attractor.

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