May  2003, 3(2): 193-200. doi: 10.3934/dcdsb.2003.3.193

Blue sky catastrophes in weakly coupled chains of reversible oscillators

1. 

Department of Mathematical Analysis and Numerical Mathematics, Comenius University, Mlynská dolina, 842 48 Bratislava

Received  July 2002 Revised  January 2003 Published  February 2003

Countable many weakly coupled reversible oscillators are investigated. Homoclinic structures are assumed for the anti-integrable limit equations. The existence of infinitely many homoclinic solutions is shown for the chains of perturbed oscillators and each of the homoclinic solutions is accumulated by continuum many breathers with periods tending to infinity. A similar result is shown for the case when heteroclinic loop structures are assumed for the anti-integrable limit equations. Applications are given to several models.
Citation: Michal Fečkan. Blue sky catastrophes in weakly coupled chains of reversible oscillators. Discrete & Continuous Dynamical Systems - B, 2003, 3 (2) : 193-200. doi: 10.3934/dcdsb.2003.3.193
[1]

Francesca Alessio, Piero Montecchiari, Andrea Sfecci. Saddle solutions for a class of systems of periodic and reversible semilinear elliptic equations. Networks & Heterogeneous Media, 2019, 14 (3) : 567-587. doi: 10.3934/nhm.2019022

[2]

Martina Chirilus-Bruckner, Christopher Chong, Oskar Prill, Guido Schneider. Rigorous description of macroscopic wave packets in infinite periodic chains of coupled oscillators by modulation equations. Discrete & Continuous Dynamical Systems - S, 2012, 5 (5) : 879-901. doi: 10.3934/dcdss.2012.5.879

[3]

D. Bonheure, C. Fabry, D. Smets. Periodic solutions of forced isochronous oscillators at resonance. Discrete & Continuous Dynamical Systems - A, 2002, 8 (4) : 907-930. doi: 10.3934/dcds.2002.8.907

[4]

Samir Adly, Daniel Goeleven, Dumitru Motreanu. Periodic and homoclinic solutions for a class of unilateral problems. Discrete & Continuous Dynamical Systems - A, 1997, 3 (4) : 579-590. doi: 10.3934/dcds.1997.3.579

[5]

Jian Wu, Jiansheng Geng. Almost periodic solutions for a class of semilinear quantum harmonic oscillators. Discrete & Continuous Dynamical Systems - A, 2011, 31 (3) : 997-1015. doi: 10.3934/dcds.2011.31.997

[6]

Carlos Garca-Azpeitia, Jorge Ize. Bifurcation of periodic solutions from a ring configuration of discrete nonlinear oscillators. Discrete & Continuous Dynamical Systems - S, 2013, 6 (4) : 975-983. doi: 10.3934/dcdss.2013.6.975

[7]

Flaviano Battelli, Ken Palmer. Transversal periodic-to-periodic homoclinic orbits in singularly perturbed systems. Discrete & Continuous Dynamical Systems - B, 2010, 14 (2) : 367-387. doi: 10.3934/dcdsb.2010.14.367

[8]

S. Secchi, C. A. Stuart. Global bifurcation of homoclinic solutions of Hamiltonian systems. Discrete & Continuous Dynamical Systems - A, 2003, 9 (6) : 1493-1518. doi: 10.3934/dcds.2003.9.1493

[9]

Shengfu Deng. Periodic solutions and homoclinic solutions for a Swift-Hohenberg equation with dispersion. Discrete & Continuous Dynamical Systems - S, 2016, 9 (6) : 1647-1662. doi: 10.3934/dcdss.2016068

[10]

André Vanderbauwhede. Continuation and bifurcation of multi-symmetric solutions in reversible Hamiltonian systems. Discrete & Continuous Dynamical Systems - A, 2013, 33 (1) : 359-363. doi: 10.3934/dcds.2013.33.359

[11]

Juntao Sun, Jifeng Chu, Zhaosheng Feng. Homoclinic orbits for first order periodic Hamiltonian systems with spectrum point zero. Discrete & Continuous Dynamical Systems - A, 2013, 33 (8) : 3807-3824. doi: 10.3934/dcds.2013.33.3807

[12]

Vera Ignatenko. Homoclinic and stable periodic solutions for differential delay equations from physiology. Discrete & Continuous Dynamical Systems - A, 2018, 38 (7) : 3637-3661. doi: 10.3934/dcds.2018157

[13]

Changrong Zhu, Bin Long. The periodic solutions bifurcated from a homoclinic solution for parabolic differential equations. Discrete & Continuous Dynamical Systems - B, 2016, 21 (10) : 3793-3808. doi: 10.3934/dcdsb.2016121

[14]

Paul H. Rabinowitz. On a class of reversible elliptic systems. Networks & Heterogeneous Media, 2012, 7 (4) : 927-939. doi: 10.3934/nhm.2012.7.927

[15]

Marc Henrard. Homoclinic and multibump solutions for perturbed second order systems using topological degree. Discrete & Continuous Dynamical Systems - A, 1999, 5 (4) : 765-782. doi: 10.3934/dcds.1999.5.765

[16]

Thomas I. Seidman, Olaf Klein. Periodic solutions of isotone hybrid systems. Discrete & Continuous Dynamical Systems - B, 2013, 18 (2) : 483-493. doi: 10.3934/dcdsb.2013.18.483

[17]

J. R. Ward. Periodic solutions of first order systems. Discrete & Continuous Dynamical Systems - A, 2013, 33 (1) : 381-389. doi: 10.3934/dcds.2013.33.381

[18]

Lixia Wang, Shiwang Ma. Unboundedness of solutions for perturbed asymmetric oscillators. Discrete & Continuous Dynamical Systems - B, 2011, 16 (1) : 409-421. doi: 10.3934/dcdsb.2011.16.409

[19]

Tianqing An, Zhi-Qiang Wang. Periodic solutions of Hamiltonian systems with anisotropic growth. Communications on Pure & Applied Analysis, 2010, 9 (4) : 1069-1082. doi: 10.3934/cpaa.2010.9.1069

[20]

Alessandro Fonda, Andrea Sfecci. Multiple periodic solutions of Hamiltonian systems confined in a box. Discrete & Continuous Dynamical Systems - A, 2017, 37 (3) : 1425-1436. doi: 10.3934/dcds.2017059

2018 Impact Factor: 1.008

Metrics

  • PDF downloads (4)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]