Absolute stability, conditional stability and bifurcation in Kolmogorov-type predator-prey systems with discrete delays

Quarterly of Applied Mathematics

Volumn 59, Issue 1, 2001, Pages 159-173

  Ruan, S ^a  

^a DALHOUSIE UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); BOUNDARY CONDITIONS; INTEGRAL EQUATIONS; LINEARIZATION; MATHEMATICAL MODELS; PARAMETER ESTIMATION; PARTIAL DIFFERENTIAL EQUATIONS; POLYNOMIALS; POPULATION STATISTICS;

ABSOLUTE STABILITY; CONDITIONAL STABILITY; DISCRETE DELAYS; HOPF BIFURCATION; KOLMOGOROV PREDATOR PREY SYSTEMS;

ASYMPTOTIC STABILITY;

EID: 0035281981     PISSN: 0033569X     EISSN: None     Source Type: Journal    
DOI: 10.1090/qam/1811101     Document Type: Article

References (45)

1. On the stability of some exponential polynomials
2. On theoretical models for competitive and predatory biological systems
3. Differential-difference equations
4. Convergence results in a well-known delayed predator-prey system
5. Stability criteria for second-order dynamical systems involving several time delays
6. Characteristic return times for harvested population models with time lag
7. Absolute stability in delay equations
8. Sur le problème biologique héréditaire de deux espèces dévorante et dévoré
9. Global attractivity in time-delayed predator-prey systems
10. Unconditional stability of systems with time-lags
11. Discrete delay, distributed delay and stability switches
12. On zeros of some transcendental equations
13. Integrodifferential equations and delay models in population dynamics
14. Nonconstant periodic solutions in predator-prey systems with continuous time delay
15. A procedure for determination of the exponential stability of certain differential difference equations
16. Foundations of modern analysis
17. Multiparameter bifurcation diagrams in predator-prey models with time lag
18. Nonoccurrence of stability switching in systems with discrete delays
19. The tradeoff between mutual interference and time lags in predator-prey systems
20. Stability criteria for a system involving two time delays
21. On the Volterra and other nonlinear models of interacting populations
22. Harmless delay in model systems
23. Delayed responses and stability in two-species systems
24. Stability and oscillations in delay differential equations of population dynamics
25. Stability in linear delay equations
26. Introduction to functional differential equations
27. Theory and applications of hopf bifurcation
28. Age-dependent predation is not a simple process: I. Continuous time models
29. Delays in recruitment at different trophic levels: Effects on stability
30. Stability and delays in a predator-prey system
31. Algebraic criteria on the stability of the zero solutions of the second order delay differential equations
32. Circular cause systems in ecology
33. Delay differential equations with applications in population dynamics
34. Global stability for two-species Lotka-Volterra systems with delay
35. Stability of predation models with time delay
36. A test for stability of linear differential delay equations
37. Time delay versus stability in population models with two and three trophic levels
38. Time lags in biological models
39. The effect of long time delays in predator-prey systems
40. Absolute stability in predator-prey models
41. On the zeros of transcendental functions with applications to stability of delay differential equations
42. Great delay in a predator-prey model
43. Leçons sur la théorie mathématique de la lutte pour la vie
44. Time lag in prey-predator population models
45. Global existence of periodic solutions in a class of delayed gause-type predator-prey systems