The Beverton-Holt dynamic equation. (English) Zbl 1138.39018
The Cushing-Henson conjectures regarding the Beverton-Holt difference equation in a periodic environment are reformulated and verified in the context of dynamic equations on time-scales.
Reviewer: Raghib Abu-Saris (Sharjah)
MSC:
| 39A12 | Discrete version of topics in analysis |
| 39A20 | Multiplicative and other generalized difference equations |
| 39A11 | Stability of difference equations (MSC2000) |
Keywords:
Cushing-Henson conjecture; time scales; dynamic equation; logistic equation; Beverton-Holt equation; Jensen inequality; periodic solutionReferences:
| [1] | Akın-Bohner E, Methods and Applications of Analysis 10 (1) pp 11– (2003) · Zbl 1076.39001 · doi:10.4310/MAA.2003.v10.n1.a2 |
| [2] | Beverton RJH, On the Dynamics of Exploited Fish Populations (1957) |
| [3] | Bi L, Nonlinear Analysis (2007) |
| [4] | Bohner M, Far East Journal of Applied Mathematics 18 (3) pp 289– (2005) |
| [5] | Bohner M, Dynamic Equations on Time Scales (2001) · doi:10.1007/978-1-4612-0201-1 |
| [6] | Bohner M, Advances in Dynamic Equations on Time Scales (2003) · Zbl 1025.34001 · doi:10.1007/978-0-8176-8230-9 |
| [7] | Cushing JM, Journal of Difference Equations and Applications 8 (12) pp 1119– (2002) · Zbl 1023.39013 · doi:10.1080/1023619021000053980 |
| [8] | Elaydi S, Journal of Differential Equations 208 (1) pp 258– (2005) · Zbl 1067.39003 · doi:10.1016/j.jde.2003.10.024 |
| [9] | Elaydi S, Journal of Difference Equations and Applications 11 (4) pp 337– (2005) · Zbl 1084.39005 · doi:10.1080/10236190412331335418 |
| [10] | Hilger S, Results in Mathematics 18 (1) pp 18– (1990) · Zbl 0722.39001 · doi:10.1007/BF03323153 |
| [11] | Kocic VL, Journal of Difference Equations and Applications 11 (4) pp 415– (2005) · Zbl 1084.39007 · doi:10.1080/10236190412331335463 |
| [12] | Kocic VL, Difference Equations and Discrete Dynamical Systems pp 101– (2005) · doi:10.1142/9789812701572_0008 |
| [13] | Kocic VL, Journal of Difference Equations and Applications 10 (13) pp 1267– (2004) · Zbl 1072.39016 · doi:10.1080/10236190410001652766 |
| [14] | Wong F-H, Advances in Dynamical Systems and Applications 1 (1) pp 113– (2006) |
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