GLOBAL ATTRACTOR OF COUPLED DIFFERENCE EQUATIONS AND APPLICATIONS TO LOTKA-VOLTERRA SYSTEMS C V doc

... (u ,v) ,thesolution(u n ,v n ) converges monotonically 78 Global attractor of difference equations Remark 5.4. The convergence of the solution (u n ,v n )to( u ∗ ,v ∗ ) for arbitrary nonnega- tive ... above hypothesis, ᏿ is given by ᏿ ≡  (u ,v) ∈ R 2 ;  δ (1) ,δ (2)  ≤ (u ,v) ≤  M (1) ,M (2)  . (2.3) GLOBAL ATTRACTOR OF COUPLED DIFFERENCE EQUATIONS AND APP...

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... z k−1 ρ k−1  z −1  , (2.16) having positive coefficients. Proof. Item (1) immediately follows by taking into account (2.11) and by using (2.13). Moreover, (2) and (3) are easy consequence of (2.14). Concerning item ... inside the unit circle and, of course, the number of conditions at the end of the interval of integ ration should be equal to the number of roots outside th...

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... periodic solutions are found for a system of delay difference equations. By using such results, the existence of nontrivial periodic solutions for delay difference equations with positive and negative termsisalsoconsidered. 1. ... Z,weknowthatu ∗ = v ∗ . (Indeed, if u ∗ = v ∗ ,then u ∗ = v ∗ = 0, which is contrar y to the fact that (u ∗ ,v ∗ ) = (0,0).) Thus u ∗ − v ∗ is...

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... 2011 References 1. Kulenovic MRS, aa, Ladas, G: Dynamics of Second Order Rational Difference Equations with Open Problems and Conjectures. Chapman & Hall/CRC Press, Boca Raton, FL. (2001) 2. Kocic, VL, ... point of Equation 1 is global attractor. In Sect. 4 we give the solutions of some special cases of Equat ion 1 and give a numeri cal exam- ples of each case and d...

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... run. References 1 J. Hill and C. Cichra, “Eradication of a reproducing population of Convict Cichlids, Cichlasoma nigrofasciatum Cichlidae in North-Central Florida,” Florida Scientist, vol. 68, ... like to conclude by reiterating that invasive species pose a clear and present danger to both the ecosystems they reside in and the regional and global economies they affect....

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... norm of a vector in E d . 2.1. Almost periodic sequences. We review definitions of (uniformly) almost periodic and asymptotically almost periodic sequences, which have been discussed by several ... Publishing Corporation Advances in Difference Equations Volume 2007, Article ID 68023, 15 pages doi:10.1155/2007/68023 Research Article Periodic and Almost Periodic Solutions of Functiona...

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... Waves, Cylindrical Waves, and Spherical Waves Cartesian Coordinates: Plane Waves Cylindrical Waves Spherical Waves Acoustic Scattering Scattering by Spheres, Cylinders, and Disks Mie Scattering ... Waves, Cylindrical Waves, and Spherical Waves Cartesian Coordinates: Plane Waves Cylindrical Waves Spherical Waves Acoustic Scattering 21 21 22 24 30 32 32 Scattering by S...

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... E .V. Voskoresenski, Asymptotic equivalence of systems of differential equations, Results of mathematic science 40 (1985) 245 (Russian). [4] M. Svec, Itegral and asymptotic equivelence of two systems ... the Conference on Mathematics, Mechanics, and Informatics, Hanoi, 7/10/2006, on the occasion of 50th Anniversary of Department of Mathematics, Mechanics and Informati...

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... mor- phology of polyethylene has improved dramatically. With the advent of perman- ganic acid etching of fractured and cut surfaces [38] and chlorosulfonic acid staining of microtomed sections [39], ... somewhat abrasive and can accelerate wear in extruders and other processing equipment. Ziegler–Natta catalyst systems invariably contain a variety of active sites due to...

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