zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Impulsive perturbations of a predator-prey system with modified Leslie-Gower and Holling type II schemes. (English) Zbl 1222.34057
The authors investigate the dynamics of an impulsively controlled predator-prey model with modified Leslie-Gower and Holling type II schemes. Choosing the pest birth rate r 1 as control parameter, the authors show that there exists a globally asymptotically stable pest-eradication periodic solution when r 1 is less than some critical value r 1 * , and the system is permanent when r 1 is larger than the critical value r 1 * . By use of standard techniques of bifurcation theory, the authors prove the existence of oscillations in pest and predator. Furthermore, some situations which lead to a chaotic behavior of the system are investigated by means of numerical simulations.
34C60Qualitative investigation and simulation of models (ODE)
34A37Differential equations with impulses
92D25Population dynamics (general)
34C25Periodic solutions of ODE
34D05Asymptotic stability of ODE
[1]Van Lenteren, J.C.: Measures of success in biological control of anthropoids by augmentation of natural enemies. In: Wratten, S., Gurr, G. (eds.) Measures of Success in Biological Control. Kluwer Academic, Dordrecht (2000)
[2]Wright, R.J.: Achieve Biological Pest Control by Augmenting Natural Enemy Populations. University of Nebraska, Crop Watch (1995)
[3]Stern, V.M., Smith, R.F., Van Den Bosch, R., Hagen, K.S.: The integrated control concept. Hilgardia 29(159), 81–101 (1959)
[4]Jiao, J., Chen, L.: Global attractivity of a stage-structure variable coefficients predator-prey system with time delay and impulsive perturbations on predators. Int. J. Biomath. 1, 197–208 (2008) · Zbl 1155.92355 · doi:10.1142/S1793524508000163
[5]Zhang, S.W., Wang, F.Y., Chen, L.S.: A food chain system with density-dependent birth rate and impulsive perturbations. Adv. Complex Syst. 9(3), 223–236 (2006) · Zbl 1107.92060 · doi:10.1142/S0219525906000781
[6]D’Onofrio, A.: Stability properties of pulse vaccination strategy in SEIR epidemic model. Math. Biosci. 179, 72–57 (2002)
[7]Jiao, J.J., Chen, L.S., Nieto, J.J., Torres, A.: Permanence and global attractivity of stage-structured predator-prey model with continuous harvesting on predator and impulsive stocking on prey. Appl. Math. Mech. (English Ed.) 29, 653–663 (2008) · Zbl 1231.34021 · doi:10.1007/s10483-008-0509-x
[8]Zeng, G., Wang, F., Nieto, J.J.: Complexity of a delayed predator-prey model with impulsive harvest and Holling type II functional response. Adv. Complex Syst. 11, 77–97 (2008) · Zbl 1168.34052 · doi:10.1142/S0219525908001519
[9]Zhang, H., Chen, L.S., Nieto, J.: A delayed epidemic model with stage-structure and pulses for pest management strategy. Nonlinear Anal.: Real World Appl. 9, 1714–1727 (2008) · Zbl 1154.34394 · doi:10.1016/j.nonrwa.2007.05.004
[10]Dong, L.Z., Chen, L.S., Sun, L.H.: Extinction and permanence of the predator-prey with stocking of prey and harvesting of predator impulsive. Math. Methods Appl. Sci. 29, 415–425 (2006) · Zbl 1086.92051 · doi:10.1002/mma.688
[11]Cushing, J.M.: Periodic time-dependent predator-prey systems. SIAM J. Appl. Math. 10, 384–400 (1977)
[12]Grebogi, C., Ott, E., Yorke, J.A.: Crises, sudden changes in chaotic attractors and chaotic transients. Physica D 7, 200–181 (1983) · Zbl 0561.58029 · doi:10.1016/0167-2789(83)90126-4