Chaos controlling self-sustained electromechanical seismograph system based on the Melnikov theory

Nonlinear Dynamics

Volumn 62, Issue 1-2, 2010, Pages 379-389

  SieweSiewe M ^a,b   Yamgoue S B ^b   MoukamKakmeni F M ^c   Tchawoua, C ^b  

^a UNIVERSITY OF PRETORIA   (South Africa)

^b UNIVERSITY OF YAOUNDÉ I   (Cameroon)

^c UNIVERSITY OF BUEA   (Cameroon)

Author keywords

Antimonotonicity; Bifurcation; Chaos; Electromechanical seismograph; Heteroclinic orbit; Homoclinic orbit; Melnikov

Indexed keywords

BIFURCATION (MATHEMATICS); CHAOS THEORY; HAMILTONIANS; PERTURBATION TECHNIQUES; SEISMOGRAPHS; SYSTEM STABILITY;

ANTI-MONOTONICITY; BOUNDEDNESS CONDITIONS; FIRST ORDER EQUATIONS; HETEROCLINIC ORBIT; HOMOCLINIC ORBITS; MELNIKOV; ONSET OF INSTABILITIES; SADDLE NODE BIFURCATION;

ELECTROMECHANICAL DEVICES;

EID: 84889091054     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-010-9725-3     Document Type: Article

References (28)

1. Rand, R.H., Holmes, P.J.: Bifurcation of periodic motions in two weakly coupled van der pol oscillators. Int. J. Non-Linear Mech. 15, 387-399 (1980).
2. Arafat, H.N., Nayfeh, A.H.: Non-linear responses of suspended cables to primary resonance excitation. J. Sound Vib. 266, 325-354 (2003).
3. Ott, E., Grebogi, C., Yorke, J.A.: Controlling chaos. Phys. Rev. Lett. 64, 1196-1199 (1990).
4. Shinbrot, T., Ott, E., Grebogi, C., Yorke, J.A.: Using small perturbations to control chaos. Nature 363, 411-417 (1993).
5. Shinbrot, T., Ott, E., Grebogi, C., Yorke, J.A.: Using chaos to direct trajectories. Phys. Rev. Lett. 65, 3215-3218 (1990).
6. Lima, R., Pettini, M.: Suppression of chaos by resonant parametric perturbations. Phys. Rev. A 41, 726-733 (1990).
7. Ramesh, M., Narayanan, S.: Chaos control by nonfeedback methods in the presence of noise. Chaos Solitons Fractals 10, 1473-1489 (1990).
8. Braiman, Y., Goldhirsch, I.: Taming chaotic dynamics with weak periodic perturbations. Phys. Rev. Lett. 20, 2545-2548 (1991).
9. Show, W., Wiggins, S.: Chaotic dynamics of a whirling pendulum. Physica D 31, 190-211 (1988).
10. Melnikov, V.K.: On the stability of the centre for timeperiodic perturbations. Trans. Mosc. Math. Soc. 12, 1-57 (1963).
11. Holmes, P.J., Marsden, J.E.: Horseshoe and Arnold diffusion for Hamiltonian system on Lie groups. Indiana Univ. Math. J. 32, 273-309 (1983).
12. Holmes, P.J., Marsden, J.E.: Horseshoes in perturbations of Hamiltonian systems with two degrees of freedom. Commun. Math. Phys. 82, 523-544 (1982).
13. Holmes, P.J., Marsden, J.E.: Melnikov's method and Arnold diffusion for perturbations of integrable Hamiltonian systems. J. Math. Phys. 23, 669-675 (1982).
14. Hegazy, U.H.: Dynamics and control of self-sustained electromechanical seismographs with time varying stiffness. Mecanica 44, 355-368 (2009).
15. Chedjou, J.C., Kyamakya, K., Moussa, I., Kuchenbecker, H.-P., Mathis, W.: Behavior of a self-sustained electromechanical transducer and routes to chaos. J. Vib. Acoust. 128, 1-12 (2006).
16. Siewe Siewe, M., Moukam Kakmeni, F.M., Bowong, S., Tchawoua, C.: Non-linear response of a self-sustained electromechanical seismographs to fifth resonance excitations and chaos control. Chaos Solitons Fractals 29, 431-445 (2006).
17. Moukam Kakmeni, F.M., Bowong, S., Tchawoua, C., Kaptouom, E.: Dynamics and chaos control in nonlinear electrostatic transducers. Chaos Solitons Fractals 21, 1093-1108 (2004).
18. Yamapi, R., Chabi Orou, J.B., Woafo, P.: Harmonic oscillations, stability and chaos control in a non-linear electromechanical system. J. Sound Vib. 259, 1253-1264 (2003).
19. Moukam Kakmeni, F.M., Bowong, S., Tchawoua, C., Kaptouom, E.: Resonance, bifurcation and chaos control in electrostatic transducers with two external periodic forces. Physica A 333, 87-105 (2004).
20. Kitio Kwuimy, C.A., Woafo, P.: Dynamics of a selfsustained electromechanical system with flexible arm and cubic coupling. Commun. Nonlinear Sci. Numer. Simul. 12, 1504-1517 (2007).
21. Kitio Kwuimy, C.A., Woafo, P.: Dynamics, chaos and synchronization of self-sustained electromechanical systems with clamped-free flexible arm. Nonlinear Dyn. 53, 201-213 (2008).
22. Ge, Z.-M., Lin, T.-N.: Chaos, chaos control and synchronization of electro-mechanical gyrostat system. J. Sound Vib. 259, 585-603 (2003).
23. Yamgoué, S.B., Kofané, T.C.: Dynamics of driven coupled oscillators with shape deformable potential. Chaos Solitons Fractals 15, 119-129 (2003).
24. Siewe Siewe, M., Moukam Kakmeni, F.M., Tchawoua, C.: Resonance oscillations and homoclinic bifurcation in a Φ6-Van der Pol oscillators. Chaos Solitons Fractals 21, 841-853 (2004).
25. Siewe Siewe, M., Moukam Kakmeni, F.M., Tchawoua, C., Woafo, P.: Bifurcations and chaos in periodically and externally driven Φ6-Van der Pol oscillators. Physica A 357, 383-396 (2005).
26. Tchoukuegno, R., Woafo, P.: Dynamics and active control of motion of a particle in a Φ6 potential with a parametric forcing. Physica D 167, 86-100 (2002).
27. Moon, F.C., Li, G.X.: Fractal basin boundaries and homoclinic orbits for periodic motions in a two-well potential. Phys. Rev. Lett. 55, 1439-1442 (1985).
28. Wolf, A., Swift, J.B., Swinney, H.L., Vastano, J.A.: Determining Lyapunov exponents from a time series. Physica D 16, 285-317 (1985).