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On a complex Duffing system with random excitation

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  • Xu, Yong
  • Xu, Wei
  • Mahmoud, Gamal M.

Abstract

In this paper, we consider a complex Duffing system subjected to nonstationary random excitation of the form, z¨(t)+2ωξz˙(t)+ω2z+ϵz(t)|z(t)|2=αF(t), where z(t) is a complex function, α=1+i, i denotes the imaginary unit, ω, ξ represent natural frequency and damping coefficient respectively, ϵ is the small perturbation parameter and nonlinearity strength, and F(t) is a random function. This equation with F(t)=0 has connection to the complex nonlinear Schrödinger equation which appears in many important fields of physics.

Suggested Citation

  • Xu, Yong & Xu, Wei & Mahmoud, Gamal M., 2008. "On a complex Duffing system with random excitation," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 126-132.
    • Handle: RePEc:eee:chsofr:v:35:y:2008:i:1:p:126-132
    DOI: 10.1016/j.chaos.2006.07.016
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    References listed on IDEAS

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    1. Xu, Yong & Xu, Wei & Mahmoud, Gamal M, 2004. "On a complex beam–beam interaction model with random forcing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(3), pages 347-360.
    2. Yong Xu & Wei Xu & Gamal M. Mahmoud, 2005. "Generating Chaotic Limit Cycles For A Complex Duffing–Van Der Pol System Using A Random Phase," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 16(09), pages 1437-1447.
    3. Mahmoud, Gamal M., 1995. "Beam-beam interaction models with a small stochastic perturbation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 216(4), pages 445-451.
    4. Mahmoud, Gamal M. & Aly, Shaban A.H., 2000. "On periodic solutions of parametrically excited complex non-linear dynamical systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 278(3), pages 390-404.
    5. Cveticanin, L., 2001. "Analytic approach for the solution of the complex-valued strong non-linear differential equation of Duffing type," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 297(3), pages 348-360.
    6. Mahmoud, Gamal M., 1998. "Approximate solutions of a class of complex nonlinear dynamical systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 253(1), pages 211-222.
    7. G. M. Mahmoud & H. A. Abdusalam & A. A. M. Farghaly, 2001. "Chaotic Behavior And Chaos Control For A Class Of Complex Partial Differential Equations," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 12(06), pages 889-899.
    8. M. Mahmoud, Gamal & A. Mohamed, Ahmed & A. Aly, Shaban, 2001. "Strange attractors and chaos control in periodically forced complex Duffing's oscillators," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 292(1), pages 193-206.
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