Chaos In Single And Double-Well Duffing Oscillators Under Certain Parametric Variations And Excitations.
ABSTRACT
This study
focuses on the generation and evolution of chaotic motions in single and
double-well Duffing oscillators under certain parametrical excitations. The
Melnikov approach and Lyapunov exponent are proposed to calculate the threshold
values for the chaotic motion in a Duffing system. The minimum and maximum
values were obtained and the dynamical behaviors showed the intersections of
manifold which was illustrated with MATHCAD software. Similar results
obtained from the two methods show that the behavior of the perturbed Duffing
oscillator is chaotic and highly unstable with repeated resonances of
successively higher periods. As a result, the functions with symmetric wells were
separated by the barrier at a point and the unperturbed system produces three
equilibria points showing similar behaviors. Also, the method of the Lyapunov
exponents narrow the range for the critical threshold values and detect
mutations in the chaotic system. Numerical simulations showed that as the
parameter was varied, repeated resonances of successively higher periods
occurred and unstable chaotic motion was observed.
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CHINENYE, G (2022). Chaos In Single And Double-Well Duffing Oscillators Under Certain Parametric Variations And Excitations.. Repository.mouau.edu.ng: Retrieved Nov 22, 2024, from https://repository.mouau.edu.ng/work/view/chaos-in-single-and-double-well-duffing-oscillators-under-certain-parametric-variations-and-excitations-7-2
GOODLUCK, CHINENYE. "Chaos In Single And Double-Well Duffing Oscillators Under Certain Parametric Variations And Excitations." Repository.mouau.edu.ng. Repository.mouau.edu.ng, 28 Nov. 2022, https://repository.mouau.edu.ng/work/view/chaos-in-single-and-double-well-duffing-oscillators-under-certain-parametric-variations-and-excitations-7-2. Accessed 22 Nov. 2024.
GOODLUCK, CHINENYE. "Chaos In Single And Double-Well Duffing Oscillators Under Certain Parametric Variations And Excitations.". Repository.mouau.edu.ng, Repository.mouau.edu.ng, 28 Nov. 2022. Web. 22 Nov. 2024. < https://repository.mouau.edu.ng/work/view/chaos-in-single-and-double-well-duffing-oscillators-under-certain-parametric-variations-and-excitations-7-2 >.
GOODLUCK, CHINENYE. "Chaos In Single And Double-Well Duffing Oscillators Under Certain Parametric Variations And Excitations." Repository.mouau.edu.ng (2022). Accessed 22 Nov. 2024. https://repository.mouau.edu.ng/work/view/chaos-in-single-and-double-well-duffing-oscillators-under-certain-parametric-variations-and-excitations-7-2