# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Global behavior of an economic model. (English) Zbl 1196.39008
Summary: The objective of this paper is to investigate some qualitative behavior of the solutions of an economic model. This is accomplished by studying a higher order difference equation where we establish some results about the boundedness, the periodicity, and the global attractivity of the solutions of this higher order difference equation and then apply the obtained results to give a complete description of global stability and the periodic character of the solutions of the model.

##### MSC:
 39A22 Growth, boundedness, comparison of solutions (difference equations) 39A23 Periodic solutions (difference equations) 39A30 Stability theory (difference equations) 39A10 Additive difference equations 91B64 Macro-economic models (monetary models, models of taxation)
Full Text:
##### References:
 [1] Agiza, H. N.; Elsadany, A. A.: Nonlinear dynamics in the cournot duopoly game with heterogeneous players. Physica A: stat mech appl 320, 512-524 (2003) · Zbl 1010.91006 [2] Jr., J. Barkley Rosser: A reconsideration of the role of discontinuity in regional economic models. Chaos, solitons & fractals 18, 451-462 (2003) · Zbl 1072.91032 [3] Clark, C. W.: A delayed recruitment model of population dynamics with an application to baleen whale population. J math biol 3, 381-391 (1976) · Zbl 0337.92011 [4] Cull, P.: Global stability of population models. Bull math biol 43, 47-58 (1981) · Zbl 0451.92011 [5] Devault, R.; Grove, E. A.; Ladas, G.; Levins, R.; Puccia, C.: Oscillation and stability in a delay model of a perennial grass. J differ equat appl 1, 173-185 (1995) · Zbl 0856.39012 [6] El-Metwally, H.; Grove, E. A.; Ladas, G.; Raidan, M.; Levins, R.: On the difference equation ”$y(n+1)=A+By(n-1)exp(-yn)$”. Nonlinear anal 47, 4623-4634 (2001) · Zbl 1042.39506 [7] El-Metwally, H.; Grove, E. A.; Ladas, G.; Voulov, H. D.: On the global attractivity and the periodic character of some difference equations. J differ equat appl 7, 837-850 (2001) · Zbl 0993.39008 [8] El-Metwally, H.; Grove, E. A.; Ladas, G.: A global convergence result with applications to periodic solutions. J math anal appl 245, 161-170 (2000) · Zbl 0971.39004 [9] El-Metwally, H.; Kulenović, M. R. S.; Hadziomerspahic, S.: Nonoscillatory solutions for system of neutral delay equation. Nonlinear anal TMA 54, 63-81 (2003) · Zbl 1029.34057 [10] Elabbasy EM, Saker SH, El-Metwally H. Oscillation and stability of nonlinear discrete models exhibiting the Allee effect. Math Slovaca, in press. · Zbl 1150.39005 [11] Elabbasy EM, El-Metwally H, Elsayed EM. On the periodic nature of some max-type difference equations. J Math Math Sciences, in press. · Zbl 1084.39004 [12] Ishiyama, K.; Saiki, Y.: Unstable periodic orbits and chaotic economic growth. Chaos, solitons & fractals 26, 33-42 (2005) · Zbl 1073.65146 [13] Lakshmikantham, V.; Trigiante, D.: Theory of difference equations: numerical methods and applications. (1988) · Zbl 0683.39001 [14] Szydowski, Marek: Time-to-build in dynamics of economic models I: Kalecki’s model. Chaos, solitons & fractals 14, 697-703 (2002) · Zbl 1008.91078 [15] Szydowski, Marek: Time to build in dynamics of economic models II: Models of economic growth. Chaos, solitons & fractals 18, 355-364 (2003) · Zbl 1056.91050 [16] Laaksonen, Matti: Oscillations in some nonlinear economic relationships. Chaos, solitons & fractals 7, 2235-2245 (1996) · Zbl 1080.91542