메뉴 건너뛰기




Volumn 10, Issue 1, 2010, Pages 279-283

Analysis of modified Van der Pol's oscillator using He's parameter-expanding methods

Author keywords

Delay; Oscillator; Parameter expanding method; Van der Pol

Indexed keywords

ANALYTICAL METHOD; DELAY; DELAYED FEEDBACK; EXACT SOLUTION; MODIFIED EQUATION; NON-LINEAR; NONLINEAR PROBLEMS; OSCILLATOR; PARAMETER-EXPANDING METHOD; PERTURBATION METHOD; SERIES EXPANSION; VAN DER POL; VAN DER POL EQUATION; VAN DER POL'S OSCILLATORS;

EID: 69249214012     PISSN: 15671739     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cap.2009.06.006     Document Type: Article
Times cited : (42)

References (25)
  • 1
    • 0032202459 scopus 로고    scopus 로고
    • Van der Pol's oscillator under delayed feedback
    • Atay F.M. Van der Pol's oscillator under delayed feedback. J. Sound Vibrat. 218 2 (1998) 333-339
    • (1998) J. Sound Vibrat. , vol.218 , Issue.2 , pp. 333-339
    • Atay, F.M.1
  • 2
    • 34250315551 scopus 로고
    • Continuous control of chaos by self-controlling feedback
    • Pyargas K. Continuous control of chaos by self-controlling feedback. Phys. Lett. A 170 (1992) 421
    • (1992) Phys. Lett. A , vol.170 , pp. 421
    • Pyargas, K.1
  • 4
    • 30644460357 scopus 로고    scopus 로고
    • Homotopy perturbation method for solving boundary value problems
    • He J.H. Homotopy perturbation method for solving boundary value problems. Phys. Lett. A 350 (2006) 87-88
    • (2006) Phys. Lett. A , vol.350 , pp. 87-88
    • He, J.H.1
  • 5
    • 17844387391 scopus 로고    scopus 로고
    • Homotopy perturbation method for bifurcation of nonlinear problems
    • He J.H. Homotopy perturbation method for bifurcation of nonlinear problems. Int. J. Non-linear Sci. Numer. Simul. 6 (2005) 207-208
    • (2005) Int. J. Non-linear Sci. Numer. Simul. , vol.6 , pp. 207-208
    • He, J.H.1
  • 6
    • 18844391045 scopus 로고    scopus 로고
    • Limit cycle and bifurcation of nonlinear problems
    • He J.H. Limit cycle and bifurcation of nonlinear problems. Chaos Soliton Fract. 26 (2005) 827-833
    • (2005) Chaos Soliton Fract. , vol.26 , pp. 827-833
    • He, J.H.1
  • 7
    • 33144478462 scopus 로고    scopus 로고
    • Assessment of homotopy perturbation and perturbation methods in heat transfer radiation equations
    • Ganji D.D., and Rajabi A. Assessment of homotopy perturbation and perturbation methods in heat transfer radiation equations. Int. Commun. Heat Mass Transf. 33 (2006) 391-400
    • (2006) Int. Commun. Heat Mass Transf. , vol.33 , pp. 391-400
    • Ganji, D.D.1    Rajabi, A.2
  • 8
    • 33751251025 scopus 로고    scopus 로고
    • Application of homotopy perturbation method in nonlinear heat conduction and convection equations
    • Rajabi A., Ganji D.D., and Taherian H. Application of homotopy perturbation method in nonlinear heat conduction and convection equations. Phys. Lett. A 360 (2007) 570-573
    • (2007) Phys. Lett. A , vol.360 , pp. 570-573
    • Rajabi, A.1    Ganji, D.D.2    Taherian, H.3
  • 9
    • 33748919061 scopus 로고    scopus 로고
    • Application of He's homotopy-perturbation method to nonlinear coupled systems of reaction-diffusion equations
    • Ganji D.D., and Sadighi A. Application of He's homotopy-perturbation method to nonlinear coupled systems of reaction-diffusion equations. Int. J. Non-linear Sci. Numer. Simul. 7 (2006) 411-418
    • (2006) Int. J. Non-linear Sci. Numer. Simul. , vol.7 , pp. 411-418
    • Ganji, D.D.1    Sadighi, A.2
  • 10
    • 33745852188 scopus 로고    scopus 로고
    • Homotopy-perturbation method for pure nonlinear differential equation
    • Cveticanin L. Homotopy-perturbation method for pure nonlinear differential equation. Chaos Soliton Fract. 30 (2006) 1221-1230
    • (2006) Chaos Soliton Fract. , vol.30 , pp. 1221-1230
    • Cveticanin, L.1
  • 11
    • 0000092673 scopus 로고    scopus 로고
    • Variational iteration method - a kind of non-linear analytical technique
    • He J.H. Variational iteration method - a kind of non-linear analytical technique. Int. J. Non-linear Mech. 34 4 (1999) 699-708
    • (1999) Int. J. Non-linear Mech. , vol.34 , Issue.4 , pp. 699-708
    • He, J.H.1
  • 12
    • 30344475545 scopus 로고    scopus 로고
    • Construction of solitary solution and compacton-like solution by variational iteration method
    • He J.H., and Wu X.H. Construction of solitary solution and compacton-like solution by variational iteration method. Chaos Soliton Fract. 29 (2006) 108-113
    • (2006) Chaos Soliton Fract. , vol.29 , pp. 108-113
    • He, J.H.1    Wu, X.H.2
  • 13
    • 30344464250 scopus 로고    scopus 로고
    • Application of variational iteration method to nonlinear differential equations of fractional order
    • Odibat Z.M., and Momani S. Application of variational iteration method to nonlinear differential equations of fractional order. Int. J. Non-linear Sci. Numer. Simul. 7 (2006) 27-34
    • (2006) Int. J. Non-linear Sci. Numer. Simul. , vol.7 , pp. 27-34
    • Odibat, Z.M.1    Momani, S.2
  • 14
    • 34249883978 scopus 로고    scopus 로고
    • Variational iteration method for construction of some compact and noncompact structures of Klein-Gordon equations
    • Yusufoglu E. Variational iteration method for construction of some compact and noncompact structures of Klein-Gordon equations. Int. J. Non-linear Sci. Numer. Simul. 8 2 (2007) 152-158
    • (2007) Int. J. Non-linear Sci. Numer. Simul. , vol.8 , Issue.2 , pp. 152-158
    • Yusufoglu, E.1
  • 15
    • 4444377082 scopus 로고    scopus 로고
    • Determination of limit cycles for strongly nonlinear oscillators
    • He J.H. Determination of limit cycles for strongly nonlinear oscillators. Phys. Rev. Lett. 90 (2003) 174301
    • (2003) Phys. Rev. Lett. , vol.90 , pp. 174301
    • He, J.H.1
  • 16
    • 33745146914 scopus 로고    scopus 로고
    • Self-excited systems: analytical determination of limit cycles
    • D'Acunto M. Self-excited systems: analytical determination of limit cycles. Chaos Soliton Fract. 30 (2006) 719-724
    • (2006) Chaos Soliton Fract. , vol.30 , pp. 719-724
    • D'Acunto, M.1
  • 17
    • 33645972898 scopus 로고    scopus 로고
    • Some asymptotic methods for strongly nonlinear equations
    • He J.H. Some asymptotic methods for strongly nonlinear equations. Int. J. Mod. Phys. B 20 (2006) 1141-1199
    • (2006) Int. J. Mod. Phys. B , vol.20 , pp. 1141-1199
    • He, J.H.1
  • 18
    • 0035601179 scopus 로고    scopus 로고
    • Bookkeeping parameter in perturbation methods
    • He J.H. Bookkeeping parameter in perturbation methods. Int. J. Non-linear Sci. Numer. Simul. 2 (2001) 257-264
    • (2001) Int. J. Non-linear Sci. Numer. Simul. , vol.2 , pp. 257-264
    • He, J.H.1
  • 19
    • 0036489498 scopus 로고    scopus 로고
    • Modified Lindstedt-Poincare methods for some strongly non-linear oscillations, Part I: expansion of a constant
    • He J.H. Modified Lindstedt-Poincare methods for some strongly non-linear oscillations, Part I: expansion of a constant. Int. J. Non-linear Mech. 37 2 (2002) 309-314
    • (2002) Int. J. Non-linear Mech. , vol.37 , Issue.2 , pp. 309-314
    • He, J.H.1
  • 20
    • 4243080805 scopus 로고    scopus 로고
    • Approximate period of nonlinear oscillators with discontinuities by modified Lindstedt-Poincare method
    • Liu H.M. Approximate period of nonlinear oscillators with discontinuities by modified Lindstedt-Poincare method. Chaos Soliton Fract. 23 2 (2005) 577-579
    • (2005) Chaos Soliton Fract. , vol.23 , Issue.2 , pp. 577-579
    • Liu, H.M.1
  • 21
    • 34250663068 scopus 로고    scopus 로고
    • He's parameter-expanding methods for strongly nonlinear oscillators
    • Xu L. He's parameter-expanding methods for strongly nonlinear oscillators. J. Comput. Appl. Math. 207 (2007) 148-154
    • (2007) J. Comput. Appl. Math. , vol.207 , pp. 148-154
    • Xu, L.1
  • 22
    • 67349260734 scopus 로고    scopus 로고
    • Frequency-amplitude relationship of nonlinear oscillators by He's parameter-expanding method
    • Tao Z.L. Frequency-amplitude relationship of nonlinear oscillators by He's parameter-expanding method. Chaos Soliton Fract. 41 2 (2009) 642-645
    • (2009) Chaos Soliton Fract. , vol.41 , Issue.2 , pp. 642-645
    • Tao, Z.L.1
  • 23
    • 0003103931 scopus 로고
    • Averaging methods for differential equations with retarded arguments and a small parameter
    • Hale J.K. Averaging methods for differential equations with retarded arguments and a small parameter. J. Differ. Eq. 2 (1966) 57-73
    • (1966) J. Differ. Eq. , vol.2 , pp. 57-73
    • Hale, J.K.1
  • 24
    • 67649124588 scopus 로고    scopus 로고
    • A comparative comparison of He's method with perturbation and numerical methods for nonlinear vibrations equations
    • Ganji D.D., Rafei M., Sadighi A., and Ganji Z.Z. A comparative comparison of He's method with perturbation and numerical methods for nonlinear vibrations equations. Int. J. Non-linear Dynam. Eng. Sci. 1 1 (2009) 1-20
    • (2009) Int. J. Non-linear Dynam. Eng. Sci. , vol.1 , Issue.1 , pp. 1-20
    • Ganji, D.D.1    Rafei, M.2    Sadighi, A.3    Ganji, Z.Z.4
  • 25
    • 67649122127 scopus 로고    scopus 로고
    • Homotopy Pade method for solving linear and nonlinear integral equations
    • Golbabai A., and Ahmadian D. Homotopy Pade method for solving linear and nonlinear integral equations. Int. J. Non-linear Dynam. Eng. Sci. 1 1 (2009) 59-66
    • (2009) Int. J. Non-linear Dynam. Eng. Sci. , vol.1 , Issue.1 , pp. 59-66
    • Golbabai, A.1    Ahmadian, D.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.