Bendixson-Dulac criteria for difference equations

Journal of Dynamics and Differential Equations

Volumn 10, Issue 4, 1998, Pages 567-575

  McCluskey, C Connell ^a   Muldowney, James S ^a  

^a UNIVERSITY OF ALBERTA   (Canada)

Author keywords

Difference equation; Periodic orbit

Indexed keywords

EID: 54649084892     PISSN: 10407294     EISSN: 15729222     Source Type: Journal    
DOI: 10.1023/A:1022677008393     Document Type: Article

References (8)

1. Bendixson, I. (1901). Sur les courbes définies par des équations différentielles, Acta Math. 24, 1-88.
2. Busenberg, S. N., and van den Driessche, P. (1993). A method for proving the nonexistence of limit cycles. J. Math. Anal. Appl. 172, 463-479.
3. Dulac, H. (1937). Recherche des cycles limites. C.R. Acad. Sci. Paris 204, 1703-1706.
4. Li, Y., and Muldowney, J. S. (1993). On Bendixson's criterion. J. Diff. Eq. 106, 27-39.
5. Li, Y., and Muldowney, J. S. (1993). Lower bounds for the Hausdorff dimension of attractors. J. Dynam. Diff. Eq. 7, 457-469.
6. Lloyd, N. G. (1979). A note on the number of limit cycles in certain two-dimensional systems. J. London Math. Soc. 20(2), 277-287.
7. Muldowney, J. S. (1990). Compound matrices and ordinary differential equations, Rocky Mt. J. Math. 20, 857-871.
8. Robinson, C. (1985). Dynamical Systems, CRC Press, Boca Raton, FL.