Strange nonlinear behaviour governed by a set of four averaged amplitude equations

Meccanica

Volumn 31, Issue 3, 1996, Pages 347-361

  Awrejcewicz, Jan ^a  

^a LODZ UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Aperiodic oscillations; Averaged equations; Bifurcation and chaos; Self oscillations; Symbolic computation

Indexed keywords

CALCULATIONS; COMPUTATIONAL METHODS; DIFFERENTIAL EQUATIONS; INTEGRAL EQUATIONS; NUMERICAL ANALYSIS; OSCILLATIONS; PARTIAL DIFFERENTIAL EQUATIONS; PERTURBATION TECHNIQUES;

APERIODIC OSCILLATIONS; AVERAGED AMPLITUDE EQUATIONS; ORDINARY DIFFERENTIAL EQUATIONS; SELF OSCILLATIONS; SYMBOLIC COMPUTATION;

DYNAMICS;

EID: 0030168915     PISSN: 00256455     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF00426995     Document Type: Article

References (17)

1. Malkin, I.G., Some Problems in the Theory of Nonlinear Oscillation. Nauka, Moscow, 1956 (in Russian).
2. Zubov, V.I., Theory of Oscillations. High School, Moscow, 1979 (in Russian).
3. Guckenheimer, J. and Holmes, P., Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. Springer, New York, 1983.
4. Arnold, V.I., Geometrical Methods in the Theory of Ordinary Differential Equations. Springer, New York, 1983.
5. Nayfeh, A.H. and Mook, D.T., Nonlinear Oscillations. Wiley Interscience, New York, 1979.
6. Nayfeh, A.H., Introduction to Perturbation Techniques. Wiley Interscience, New York, 1981.
7. Bajaj, A.K. and Johnson, J.M., 'Asymptotic techniques and complex dynamics in weakly non-linear forced mechanical systems', Intern. J. Non-Linear Mechanics, 25(2/3) (1990) 211-226.
8. Awrejcewicz, J., 'Determination of the limits of the unstable zones of the unstationary non-linear systems', Intern. J. Non-Linear Mechanics, 23(1) (1988) 87-94.
9. Awrejcewicz, J., 'Determination of periodic oscillations in non-linear autonomous discrete-continuous systems with time delay', Intern. J. Solids and Structures, 27(7) (1991) 825-832.
10. Awrejcewicz, J. and Someya, T., 'Analytical condition for the existence of two-parameter family of periodic orbits in the autonomous system', J. Physic. Soc. Japan, 60(3) (1991) 781-784.
11. Newell, A.C. and Whitehead, J.A., 'Finite bandwidth, finite amplitude convection', J. Fluid Mech., 38(2) (1969) 279-303.
12. Awrejcewicz, J., 'Analytical and numerical study of nonlinear behaviour of the electromechanical system', J. Tech. Physics, 34(1) (1993) 57-68.
13. Awrejcewicz, J., 'Nonlinear oscillations of the string caused by the electromagnetic field', in: Proceedings of the Third Polish-Japanese Seminar on Modelling and Control of Electromagnetic Phenomena, Kazimierz, April 19-21, 1993, pp. 125-128.
14. Elsgolc, L. E., Introduction to the Theory of Differential Equations with a Delay, Moscow, Nauka, 1964 (in Russian).
15. Rubanik, W.P., Oscillations in Complex Quasilinear Systems with Delay, University Press, Minsk, 1985 (in Russian).
16. Seydel, R., From Equilibrium to Chaos. Practical Bifurcation and Stability Analysis, Elsevier, New York, 1988.
17. Awrejcewicz, J., Bifurcation and Chaos in Coupled Oscillators, World Scientific, Singapore, 1991.