Asymptotic behaviour of solutions of Lotka–Volterra systems

Baris, J.; Baris, P.; Wawiórko, E.

doi:10.1016/j.nonrwa.2005.03.022

Cited by 4 publications

(3 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The results of this paper may be considered as continuation and generalization of the results obtained in [1][2][3]. Our approach can be applied to systems of partial differential equations.…”

Section: Introductionmentioning

confidence: 66%

“…Also in his monograph [12] D.H. Jacobson investigated these problems for autonomous quadratic differential systems. For nonautonomous differential systems problems (i) and (ii) are studied in [1][2][3]. In some other classes of differential equations and systems the blow-up phenomena have been studied by many authors (see, for example, [4][5][6][9][10][11][13][14][15][16][17] and references therein).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Blow-up solutions of cubic differential systems

Baris

Wawiórko

2008

Journal of Mathematical Analysis and Applications

Self Cite

View full text Add to dashboard Cite

We investigate the existence problem for blow-up solutions of cubic differential systems. We find sets of initial values of the blow-up solutions. We also discuss a method of finding upper estimates for the blow-up time of these solutions. Our approach can be applied to systems of partial differential equations. We apply this approach to the Cauchy-Dirichlet problem for systems of semilinear heat equations with cubic nonlinearities.

show abstract

Section: Introductionmentioning

confidence: 66%

Section: Introductionmentioning

confidence: 99%

Blow-up solutions of cubic differential systems

Baris

Wawiórko

2008

Journal of Mathematical Analysis and Applications

Self Cite

View full text Add to dashboard Cite

show abstract

“…Many excellent results concerned with the permanence, extinction and global attractivity of partial species for system (1) were obtained, see [1][2][3][4][5]10,11,[21][22][23][24] and the references cited therein.…”

Section: §1 Introductionmentioning

confidence: 99%

Partial extinction, permanence and global attractivity in nonautonomous n-species Lotka-Volterra competitive systems with impulses

Hou

Teng

Gao

2011

Appl. Math. J. Chin. Univ.

View full text Add to dashboard Cite

In this paper, the qualitative properties of general nonautonomous Lotka-Volterra n-species competitive systems with impulsive effects are studied. Some new criteria on the permanence, extinction and global attractivity of partial species are established by used the methods of inequalities estimate and Liapunov functions. As applications, nonautonomous two species Lotka-Volterra systems with impulses are discussed. §1 IntroductionIn the natural world, competition is usually defined as the simultaneous demand by two or more organisms for limited environmental resources, such as food, nutrients, living space, or light. As there are two sides to everything , competition can be good to the natural selection, but on the other hand, it is harmful to some cases. For multiple species in a habitat, one well-known consequence of competition is that all species will be co-prosperous; the another consequence is partial species can coexist and segmental species will be extinct. Modeling and analysis of the dynamics of biological populations by means of differential equations is one of the primary concerns in population growth problems. As we well known, Lotka-Volterra competition system which models the interaction among various competing species is one of the most celebrated models in mathematical biology and population dynamics. Traditional Lotka-Volterra competition system usually is expressed as follows:a ij (t)x j (t)], i = 1, 2, · · · , n.

show abstract

On blow-up solutions of polynomial Kolmogorov systems

Baris

Wawiórko

2008

Nonlinear Analysis: Real World Applications

View full text Add to dashboard Cite

Asymptotic behaviour of solutions of Lotka–Volterra systems

Cited by 4 publications

References 12 publications

Blow-up solutions of cubic differential systems

Blow-up solutions of cubic differential systems

Partial extinction, permanence and global attractivity in nonautonomous n-species Lotka-Volterra competitive systems with impulses

On blow-up solutions of polynomial Kolmogorov systems

Contact Info

Product

Resources

About