Generalization of Lotka-Volterra, GLV, systems with some dynamical and topological properties

Chaos, solitons and fractals

Volumn 11, Issue 11, 2000, Pages 1747-1751

  El Rifai, E A ^a  

^a Mansoura University   (Egypt)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL MODELS; TOPOLOGY;

GENERALIZED LOTKA-VOLTERRA (GLV) MODEL;

CHAOS THEORY;

EID: 0033736935     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(99)00058-2     Document Type: Article

References (16)

1. Birman J., Williams R.F. Knotted periodic orbits in dynamical systems: Lorenz's equations. Topology. 22:1983;47.
2. Walf A., Swift J., Swinney H., Vastano J. Determining Lyapunov exponents from a time series. Physica D. 16:1985;285.
3. Rossler O.E. Different types of chaos in two simple differential equations. Z Naturforsch. 31A:1976;1664.
4. King R.B. The flow topology of chemical reaction networks. J Theor Biol. 98:1982;347.
5. Edelstein-Keshet L. Mathematical models in biology. USA: Random House, 1988.
6. West BJ. Fractals and chaos in medicine. Singspore: World Scientific, 1990.
7. Rossler O.E. An equation for hyperchaos. Phys Lett. 71A:1979;155.
8. Lorenz E.N. Deterministic nonperiodic flow. J Atmos Sci. 20:1963;130.
9. El-Rifai E.A. Necessary and sufficient condition for Lorenz knots to be closed under satellite construction. Chaos, Solitons and Fractals. 10(1):1999;137-146.
10. El-Rifai EA, Ahmed EA. Knotted periodic orbits in Rossler's equation. J Math Phys 1995;36(2).
11. Adams C., El Naschie M.S. Knot theory and its applications. Chaos, Solitons and Fractals. 9(415):1998.
12. MacDonald N. Tree and networks in biological models. New York: Wiley, 1983.
13. Ghrist RW, Holmes PJ, Sullivan MC. Knots and links in three-dimensional flows. Lecture notes in mathematics, vol. 1654. Berlin: Springer, 1997.
14. Burde G. Zieschang H. Knots. Berlin: De Gruyter, 1985.
15. Sachdev P.L., Sarathy R. Periodic and chaotic solutions for a nonlinear system arising from a nuclear spin generator. Chaos, Solitons and Fractals. 4(11):1994.
16. Birman J. Braids and links. USA: Publish or Perish, 1976.