Bifurcations of cycles in systems of differential equations with a finite symmetry group - II

Journal of Dynamical and Control Systems

Volumn 4, Issue 3, 1998, Pages 343-363

  Nikolaev, E V ^a   Shnol, E E ^a  

^a INSTITUTE OF MATHEMATICAL PROBLEMS OF BIOLOGY   (Russian Federation)

Author keywords

Bifurcation; Differential equation; Limit cycle; Symmetry group

Indexed keywords

BIFURCATION (MATHEMATICS); EIGENVALUES AND EIGENFUNCTIONS; MATHEMATICAL TRANSFORMATIONS; NUMERICAL ANALYSIS; POLYNOMIALS; DIFFERENTIAL EQUATIONS;

FINITE SYMMETRY GROUP; LIMIT CYCLE; SYMMETRIC CYCLES; SYMMETRY TRANSFORMATIONS;

DIFFERENTIAL EQUATIONS; BIFURCATION (MATHEMATICS);

EID: 0032116665     PISSN: 10792724     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022884316030     Document Type: Article

References (14)

1. E. V. Nikolaev and E. E. Shnol, Bifurcations of cycles in systems of differential equations with a finite symmetry group. I. J. Dynam. and Control Syst. 4 (1998), No. 3, 315-341.
2. V. I. Arnold, Geometrical methods in the theory of ordinary differential equations. In: A Series of Comprehensive Studies in Math., Vol. 250. Springer, New York, 1983.
3. J. Guckenheimer and Ph. Holmes, Nonlinear oscillations, dynamical systems and bifurcations of vector fields. Appl. Math. Sci. 42 (1986).
4. V. S. Afraimovich, V. I. Arnold, Yu. S. Il'yashenko, and L. P. Shilnikov, Bifurcation theory. In: Dynamical Systems-5, Encyclopaedia of Mathematical Sciences, V. I. Arnold, Ed., Springer, Berlin, 1994.
5. Yu. A. Kuznetsov, Elements of Applied Bifurcation Theory. Appl. Math. Sci. 112 (1995).
6. M. Golubitsky, I. Stewart, and D. G. Schaeffer, Singularities and groups in bifurcation theory. II. Appl. Math. Sci. 69 (1988).
7. B. Werner, Eigenvalue problems with the symmetry of a group and bifurcations. In: Continuation and Bifurcations: Numerical Techniques and Applications, D. Roose, B. De Dier, and A. Spence, Eds. NATO ASI Series, Series C: Mathematical and Physical Sciences, Vol. 313. Kluwer Academic Publishers, 1990, 71-88.
8. D. Ruelle, Bifurcations in the presence of a symmetry group. Arch. Rational Mech. Anal. 51 (1973), 136-152.
9. E. E. Shnol and E. V. Nikolaev, Bifurcations of equilibria in systems of differential equations with a finite symmetry group. (Russian) Preprint: Institute for Mathematical Problems in Biology, Academy of Sciences of Russian Federation (Pushchino), 1997.
10. P. Chossat and M. Golubitsky, Iterates of maps with symmetry. SIAM J. Math. Anal. 19 (1988), No. 6, 1259-1270.
11. M. W. Hirsch, C. C. Pugh, and M. Shub, Invariant manifolds. Springer, Berlin, 1977.
12. Yu. A. Kuznetsov, Andronov-Hopf bifurcation in a four-dimensional system with the circular symmetry. (Russian) Preprint: Research Computing Centre, USSR Academy of Sciences (Pushchino), 1984.
13. B. Fiedler, Global bifurcation of periodic solutions with symmetry. Lect. Notes Math. 1309 (1988).
14. E. V. Nikolaev, Bifurcations of limit cycles of differential equations possessing a finite symmetry group. (Russian) PhD Thesis: Nizhegorod State University, Nizhnii Novgorod, 1995.