Isochronous Liénard-type nonlinear oscillators of arbitrary dimensions

详细信息    查看全文

• 作者：AJEY K TIWARI ; A DURGA DEVI ; R GLADWIN PRADEEP ; V K CHANDRASEKAR
• 关键词：Isochronous system ; Liénard ; type system ; singular and nonsingular Hamiltonian.
• 刊名：Pramana
• 出版年：2015
• 出版时间：November 2015
• 年：2015
• 卷：85
• 期：5
• 页码：789-805
• 全文大小：228 KB
• 参考文献：[1]M Lakshmanan and S Rajasekar, Nonlinear dynamics: Integrability, chaos and patterns (Springer-Verlag, Berlin, 2003)CrossRef
  [2]R Grimshaw, Nonlinear ordinary differential equations (CRC Press, Boca Raton, 2000)
  [3]F Verhulst, Nonlinear differential equations and dynamical systems (Springer-Verlag, Berlin, 2000)
  [4]S Wiggins, Introduction to applied nonlinear dynamical systems and chaos (Springer, New York, 2003)MATH
  [5]S H Strogatz, Nonlinear dynamics and chaos with applications to physics, biology, chemistry and engineering (Perseus Books, Cambridge, Massachusetts, 1994)
  [6]E A Jackson, Perspectives of nonlinear dynamics (Cambridge University Press, Cambridge, 1991)MATH
  [7]R C Hilborn, Chaos and nonlinear dynamics: An introduction for scientists and engineers (Oxford University Press, New York, 2000)CrossRef
  [8]A Medio and M Lines, Nonlinear dynamics: A primer (Cambridge University Press, Cambridge, 2001)CrossRef
  [9]F Calogero, Isochronous systems (Oxford University Press, USA, 2008)MATH CrossRef
  [10]A H Nayfeh and D T Mook, Nonlinear oscillations (Wiley, New York, 1979)MATH
  [11]M Lakshmanan and V K Chandrasekar, Eur. Phys. J.: Special Topics 222, 665 (2013)ADS
  [12]F Calogero, J. Math. Phys. 38, 5711 (1997)MATH MathSciNet CrossRef ADS
  [13]F Calogero and F Leyvraz, J. Math. Phys. 47, 042901 (2006)MathSciNet CrossRef ADS
  [14]F Calogero and F Leyvraz, J. Phys. A: Math. Theor. 39, 11803 (2006); 40, 12931 (2007); 41, 175202 (2008)
  [15]F Calogero and F Leyvraz, J. Nonlinear Math. Phys. 14, 612 (2007)MATH MathSciNet CrossRef ADS
  [16]Ajey K Tiwari, S N Pandey, M Senthilvelan and M Lakshmanan, J. Math. Phys. 54, 053506 (2013); 55, 059901 (2014)
  [17]V K Chandrasekar, M Senthilvelan and M Lakshmanan, J. Phys. A: Math. Gen. 40, 4717 (2007)MATH MathSciNet CrossRef ADS
  [18]P M Mathews and M Lakshmanan, Quart. Appl. Math. 32, 215 (1974)MATH MathSciNet
  [19]P M Mathews and M Lakshmanan, Nuovo Cimento A 26, 299 (1975)MathSciNet CrossRef ADS
  [20]R Gladwin Pradeep, V K Chandrasekar, M Senthilvelan and M Lakshmanan, J. Math. Phys. 50, 052901 (2009)MathSciNet CrossRef ADS
  [21]M Lakshmanan and K Eswaran, J. Phys. A 8, 1658 (1975)CrossRef ADS
  [22]A Bhuvaneswari, V K Chandrasekar, M Senthilvelan and M Lakshmanan, J. Math. Phys. 53, 073504 (2012)MathSciNet CrossRef ADS
  [23]J F Cariñena, M F Rañada, M Santander and M Senthilvelan, Nonlinearity 17, 1941 (2004)MATH MathSciNet CrossRef ADS
  [24]J F Cariñena, M F Rañada and M Santander, Rep. Math. Phys. 54, 285 (2004)MATH MathSciNet CrossRef ADS
  [25]A R Chouikha, J. Math. Anal. Appl. 331, 358 (2007)MATH MathSciNet CrossRef
  [26]M Sabatini, J. Diff. Eq. 196, 151 (2004)MATH MathSciNet CrossRef ADS
  [27]I Boussaada, A R Chouikha and J M Strelcyn, Bull. Sci. Math. 135, 89 (2011)MATH MathSciNet CrossRef
  [28]M Bardet, I Boussaada, A R Chouikha and J M Strelcyn, Bull. Sci. Math. 135, 230 (2011)MATH MathSciNet CrossRef
  [29]Ajey K Tiwari, S N Pandey, M Senthilvelan and M Lakshmanan, submitted to Appl. Math. Comp.
  [30]E L Incé, Ordinary differential equations (Dover Publications, New York, 1944)MATH
  [31]R G Pradeep, V K Chandrasekar, M Senthilvelan and M Lakshmanan, J. Math. Phys. 51, 033519 (2010)MathSciNet CrossRef ADS
  [32]José F Cariñena, Partha Guha and Javier de Lucas, SIGMA 9, 026 (2013)
  [33]B Gambier, Acta Math. 33, 1 (1910)MathSciNet CrossRef
  [34]B van der Pol, Edinbourgh Dublin Phil. Mag. 3, 65 (1927)CrossRef
  [35]A Liénard, Rev. Gén. Electr. 23, 901 (1928)
  [36]H N Moreira, Ecol. Model. 60, 139 (1992)CrossRef
  [37]S N Pandey, P S Bindu, M Senthilvelan and M Lakshmanan, J. Math. Phys. 50, 082702 (2009); 50, 102701 (2009)
  [38]W Sarlet, F M Mahomed and P G L Leach, J. Phys. A: Math. Gen. 20, 277 (1987)MATH MathSciNet CrossRef ADS
  [39]L G S Duarte, S E S Duarte and I Moreira, J. Phys. A: Math. Gen. 20, L701 (1987)MATH MathSciNet CrossRef ADS
  [40]P G L Leach, M R Feix and S Bouquet, J. Math. Phys. 29, 2563 (1988)MATH MathSciNet CrossRef ADS
  [41]V K Chandrasekar, M Senthilvelan and M Lakshmanan, Phys. Rev. E 72, 066203 (2005)CrossRef ADS
  [42]V K Chandrasekar, A Kundu, M Senthilvelan and M Lakshmanan, J. Phys. A: Math. Gen. 39, 9743 (2006); 39, 10945 (2006)
  [43]E C G Sudarshan and N Mukunda, Classical dynamics: A modern perspective (John Wiley & Sons, New York, 1974)MATH
  [44]A Durga Devi, R Gladwin Pradeep, V K Chandrasekar and M Lakshmanan, J. Nonlinear Math. Phys. 20, 78 (2013)MathSciNet CrossRef
  [45]R Gladwin Pradeep, V K Chandrasekar, M Senthilvelan and M Lakshmanan, J. Phys. A: Math. Theor. 42, 135206 (2009)MathSciNet CrossRef ADS
  [46]C M Bender, arXiv:quant-ph/​0501052
  [47]A Durga Devi, R Gladwin Pradeep, V K Chandrasekar and M Lakshmanan, to be published
  [48]V K Chandrasekar, Jane H Sheeba, R Gladwin Pradeep, R S Divyashree and M Lakshmanan, Phys. Lett. A 376, 2188 (2012)MATH CrossRef ADS
  
• 作者单位：AJEY K TIWARI (1)
  A DURGA DEVI (1)
  R GLADWIN PRADEEP (2)
  V K CHANDRASEKAR (3)
  
  1. Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirapalli, 620 024, India
  2. Department of Physics, KCG College of Technology, Karapakkam, Chennai, 600 097, India
  3. Centre for Nonlinear Science and Engineering, School of Electrical and Electronics Engineering, SASTRA University, Thanjavur, 613 401, India
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Physics
  Astronomy
  Astrophysics
  
• 出版者：Springer India
• ISSN：0973-7111

文摘

In this paper, we briefly present an overview of the recent developments made in identifying/generating systems of Liénard-type nonlinear oscillators exhibiting isochronous properties, including linear, quadratic and mixed cases and their higher-order generalizations. There exists several procedures/methods in the literature to identify/generate isochronous systems. The application of local as well as nonlocal transformations and Ω-modified Hamiltonian method in identifying and generating systems exhibiting isochronous properties of arbitrary dimensions is also discussed in detail. The identified oscillators include singular and nonsingular Hamiltonian systems and PT-symmetric systems.