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A direct method for the numerical computation of bifurcation points underlying symmetries

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  • Attili, Basem S.

Abstract

A direct method for the numerical computation of pitchfork bifurcation points under certain symmetry conditions is presented. We will be interested in computing the critical parameter. The direct method presented produces a larger system of full rank and hence solvable. The presence of symmetry will be of help since it will reduce the amount of work needed. Numerical experimentation will be done to demonstrate the efficiency of the suggested approach.

Suggested Citation

  • Attili, Basem S., 2009. "A direct method for the numerical computation of bifurcation points underlying symmetries," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1545-1551.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:3:p:1545-1551
    DOI: 10.1016/j.chaos.2007.09.036
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    References listed on IDEAS

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    1. Sofroniou, Anastasia & Bishop, Steven R., 2006. "Breaking the symmetry of the parametrically excited pendulum," Chaos, Solitons & Fractals, Elsevier, vol. 28(3), pages 673-681.
    2. Peng, Mingshu, 2005. "Symmetry breaking, bifurcations, periodicity and chaos in the Euler method for a class of delay differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1287-1297.
    3. Jing, Zhujun & Yang, Zhiyan & Jiang, Tao, 2006. "Complex dynamics in Duffing–Van der Pol equation," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 722-747.
    4. Cao, Hongjun & Seoane, Jesús M. & Sanjuán, Miguel A.F., 2007. "Symmetry-breaking analysis for the general Helmholtz–Duffing oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 197-212.
    5. Varela, S & Masoller, C & Sicardi, A.C, 2000. "Numerical simulations of the effect of noise on a delayed pitchfork bifurcation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 283(1), pages 228-232.
    6. Bishop, S.R. & Sofroniou, A. & Shi, P., 2005. "Symmetry-breaking in the response of the parametrically excited pendulum model," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 257-264.
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    Cited by:

    1. Makenne, Y.L. & Kengne, R. & Pelap, F.B., 2019. "Coexistence of multiple attractors in the tree dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 70-82.

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