Invariant integral and the transition to steady states in separable dynamical systems

Physical Review Letters

Volumn 85, Issue 1, 2000, Pages 62-65

  Lippi, G L ^a   Barland, S ^a   Monsieur, F ^a,b  

^a UNIVERSITÉ CÔTE D'AZUR   (France)

^b Central R and D   (France)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; ASYMPTOTIC STABILITY; INTEGRAL EQUATIONS; LASERS; NONLINEAR SYSTEMS; OPTIMIZATION;

BILINEAR COUPLING; FIXED POINTS; INVARIANT INTEGRAL; SEPARABLE DYNAMICAL SYSTEMS; TEMPORAL VARIABLES;

DYNAMICS;

EID: 0034229831     PISSN: 00319007     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevLett.85.62     Document Type: Article

References (11)

1. See, e.g., the special issue on Control of Chaos: New Perspective in Experimental and Theoretical Nonlinear Science, edited by F. T. Arecchi et al. [Int. J. Bifurcation Chaos Appl. Sci. Eng. 8 (1998)], and references therein.
2. See, e.g., D. Kaplan and L. Glass, Understanding Nonlinear Dynamics (Springer, Berlin, 1995).
3. J. M.T. Thompson and H. B. Stewart, Nonlinear Dynamics and Chaos (Wiley, New York, 1986).
4. J. R. Tredicce, F. T. Arecchi, G. L. Lippi, and G. P. Puccioni, J. Opt. Soc. Am. B 2, 173 (1985).
5. A. E. Siegman, Lasers (University Science Books, Mill Valley, CA, 1986).
6. P. A. Porta, L. M. Hoffer, H. Grassi, and G. L. Lippi, Int. J. Bifurcation Chaos Appl. Sci. Eng. 8, 1811 (1998).
7. -15) as an initial condition, such that both analytical and numerical integrations be meaningful. This value "simulates" fluctuations which perturb the system away from A. However, we do not intend to reproduce by these means any stochastic effect, of no concern for this work.
8. k).
9. We do not examine the case of the node, since it is physically uninteresting.
10. In all practical cases, it will suffice to reduce the amplitude of the oscillations below the noise level to make the transition appear to have occurred without oscillations.
11. G. L. Lippi, P. A. Porta, L. M. Hoffer, and H. Grassi, Phys. Rev. E 59, R32 (1999).