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)
Positive periodic solutions in delayed Gause-type predator-prey systems. (English) Zbl 1137.34033
Based on the continuation theorem of coincidence degree theory, the authors obtain some criteria for the existence of positive periodic solutions in delayed Gause-type predator systems.
MSC:
34K13Periodic solutions of functional differential equations
92D25Population dynamics (general)
34C60Qualitative investigation and simulation of models (ODE)
References:
[1]Aghajani, A.; Moradifam, A.: Nonexistence of limit cycles in two classes of predator – prey systems, Appl. math. Comput. 175, 356-365 (2006) · Zbl 1097.34034 · doi:10.1016/j.amc.2005.07.057
[2]Allee, W. C.: Animal aggregation, Quart. rev. Biol. 2, 367-398 (1927)
[3]Fan, M.; Wang, K.: Global existence of positive periodic solution of a predator – prey system with Holling type II functional response, Acta math. Sci. ser. A chin. Ed. 21, No. 4, 492-497 (2001) · Zbl 0997.34063
[4]Freedman, H. I.; Wu, J.: Periodic solutions of single species models with periodic delay, SIAM J. Math. anal. Appl. 23, 689-701 (1992) · Zbl 0764.92016 · doi:10.1137/0523035
[5]Gaines, R. E.; Mawhin, J. L.: Coincidence degree and nonlinear differential equations, (1977)
[6]Gilpin, M. E.; Ayala, F. G.: Global models of growth and competition, Proc. natl. Acad. sci. USA 70, 3590-3593 (1973) · Zbl 0272.92016 · doi:10.1073/pnas.70.12.3590
[7]Gopalsamy, K.; Ladas, G.: On the oscillation and asymptotic behavior of N˙(t)=N(t)[a+bN(t-τ)-cn2(t-τ)], Qurt. appl. Math. 3, 433-440 (1990)
[8]Hasik, K.: Uniqueness of limit cycles in predator – prey system: the role of weight functions, J. math. Anal. appl. 277, 130-141 (2003) · Zbl 1025.34028 · doi:10.1016/S0022-247X(02)00515-2
[9]Hsu, S. B.; Huang, T. W.: Global stability for a class of predator – prey systems, SIAM J. Math. appl. 55, 763-783 (1995) · Zbl 0832.34035 · doi:10.1137/S0036139993253201
[10]Hu, X.; Liu, G.; Yan, J.: Existence of multiple positive periodic solutions of delayed predator – prey models with functional responses, Comput. math. Appl. 52, 1453-1462 (2006) · Zbl 1128.92047 · doi:10.1016/j.camwa.2006.08.030
[11]Hwang, T. W.: Uniqueness of the limit cycle for predator – prey systems, J. math. Anal. appl. 238, 179-195 (1999) · Zbl 0935.34023 · doi:10.1006/jmaa.1999.6520
[12]Kooij, R. E.; Zegeling, A.: Qualitative properties of two-dimensional predator – prey systems, Nonlinear anal. 6, 693-715 (1997) · Zbl 0883.34040 · doi:10.1016/S0362-546X(96)00068-5
[13]Kuang, Y.: Delay differential equations with applications in population dynamics, (1993) · Zbl 0777.34002
[14]Kuang, Y.: Global stability of gause-type predator – prey systems, J. math. Biol. 28, 463-474 (1990) · Zbl 0742.92022 · doi:10.1007/BF00178329
[15]Li, Y.; Kuang, Y.: Periodic solutions of periodic delay Lotka – Volterra equations and systems, J. math. Anal. appl. 255, 260-280 (2001) · Zbl 1024.34062 · doi:10.1006/jmaa.2000.7248
[16]Smith, F. E.: Population dynamics in daphnia magna and a new model for population growth, Ecology 44, 651-663 (1963)
[17]Sugie, J.: Two parameters bifurcation in a predator – prey system of ivlev type, J. math. Anal. appl. 222, 349-371 (1998) · Zbl 0894.34025 · doi:10.1006/jmaa.1997.5700
[18]Ye, D.; Fan, M.; Zhang, W.: Existence of nontrivial positive periodic solution of a predator – prey system with Holling type II functional response, Chinese J. Eng. math. 21, No. 4, 504-508 (2004) · Zbl 1083.34522
[19]Zhao, C. J.: On a periodic predator – prey system with time delays, J. math. Anal. appl. 331, 978-985 (2007) · Zbl 1140.34423 · doi:10.1016/j.jmaa.2006.09.018