ISSN:
1618-3932
Keywords:
Non-periodic oscillation
;
competitive
;
prey-predator
;
Lotka-Volterra systems
;
population biology
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Competitive systems defined by Lotka-Volterra equations (I) $$\dot x_i = x_i \left( {r_i - \sum\limits_{j = 1}^n {a_{ij} x_j } } \right),i = 1,2,...n,$$ wherer i〉0,a ij〉0, have been extensively studied in the literature. Much attention has been drawn to, among other things, the non-periodic oscillation phenomenon, or May-type trajectory as it is called by some authors, since the discovery of that kind of trajectories in competitive Lotka-Volterra systems made by May and Leonard[2]. Recently, the same phenomenon was reported to be existing in prey-predator systems. In this paper it is clear that one can expect the appearance of such phenomenon in a broader class of Lotka-Volterra systems, namely quasi-competitive systems (i.e.r i〉0. (a ij/ajj)+(a ji/aii)〉0 in (I)), which cover both competitive and some prey-predator systems in addition to others. Conditions are established in terms of the parameters of the systems for the existence of stable equilibrium, periodic oscillation and non-periodic oscillation.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02007173
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