Dynamic complexities in a parasitoid-host-parasitoid ecological model. (English) Zbl 1197.37127
Summary: Chaotic dynamics have been observed in a wide range of population models. In this study, the complex dynamics in a discrete-time ecological model of parasitoid-host-parasitoid are presented. The model shows that the superiority coefficient not only stabilizes the dynamics, but may strongly destabilize them as well. Many forms of complex dynamics were observed, including pitchfork bifurcation with quasi-periodicity, period-doubling cascade, chaotic crisis, chaotic bands with narrow or wide periodic window, intermittent chaos, and supertransient behavior. Furthermore, computation of the largest Lyapunov exponent demonstrated the chaotic dynamic behavior of the model.
Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.
Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.
References:
| [1] | May, R. M., Simple mathematical models with very complicated dynamics, Nature, 261, 459-467 (1976) · Zbl 1369.37088 |
| [2] | Ricker, W. E., Stock and recruitment, J Fish Res Board Can, 11, 559-623 (1954) |
| [3] | Xiao, Y. N.; Cheng, D. Z.; Tang, S. Y., Dynamic complexities in predator-prey ecosystem models with age-structure for predator, Chaos Solitons & Fractals, 14, 1403-1411 (2002) · Zbl 1032.92033 |
| [4] | Comins, H. N.; Hassell, R. M.; May, R. M., The spatial dynamics of host-parasitoid systems, J Anim Ecol, 61, 735-748 (1992) |
| [5] | Kaitala, V.; Ylikarjula, J.; Heino, M., Dynamic complexities in host-parasitoid interaction, J Theor Biol, 197, 331-341 (1999) |
| [6] | Castro-e-silva, A.; Bernardes, A. T., Analysis of chaotic behavior in the population dynamics, Physica A, 301, 63-70 (2001) · Zbl 1012.92033 |
| [7] | Li, Z. Q.; Wang, W. M.; Wang, H. L., Dynamics of a bedding-type system with impulsive control strategy, Chaos Solitons & Fractals, 29, 1229-1239 (2006) · Zbl 1142.34305 |
| [8] | Wang, F. Y.; Hao, C. P.; Chen, L. S., Bifurcation and chaos in a Monod-Haldene type food chain chemostat with pulsed input and washout, Chaos Solitons & Fractals, 32, 181-194 (2007) · Zbl 1130.92058 |
| [9] | Liu, B.; Teng, Z. D.; Chen, L. S., Analysis of a predator-prey model with Holling II functional response concerning impulsive control strategy, J Comput Appl Math, 193, 347-362 (2006) · Zbl 1089.92060 |
| [10] | Cavalieri, L. F.; Kocak, H., Comparative dynamics of three models for host-parasitoid interactions in a patchy environment, Bull Math Biol, 61, 141-155 (1999) · Zbl 1323.92158 |
| [11] | Xu, C. L.; Boyce, M. S., Dynamic complexities in a mutual interference host-parasitoid model, Chaos, Solitons & Fractals, 24, 175-182 (2005) · Zbl 1066.92056 |
| [12] | Killingback, T.; Blok H, J.; Doebeli, M., Scale-free extinction dynamics in spatially structured host-parasitoid systems, J Theor Biol, 241, 745-750 (2006) · Zbl 1447.92347 |
| [13] | Tang, S. Y.; Chen, L. S., Chaos in functional response host-parasitoid ecosystem models, Chaos Solitons & Fractals, 13, 875-884 (2002) · Zbl 1022.92042 |
| [14] | Garrilets, S.; Hastings, A., Intermittency and transient chaos from simple frequency-dependent selection, Proc Royal Soc London B, 261, 233-238 (1995) |
| [15] | Cavalieri, L. G.; Kocak, H., Intermittent transition between order and chaos in an inset pest population, J Theor Biol, 175, 231-234 (1995) |
| [16] | Hasting, A.; Higgins, K., Persistence of transients in spatially structured ecological models, Science, 263, 1133-1136 (1994) |
| [17] | Grond, F.; Diebner, H. H.; Sahle, S.; Mathias, A., A robust, locally interpretable algorithm for Lyapunov exponents, Chaos Solitions & Fractals, 16, 841-852 (2003) |
| [18] | Sportt, J. G., Chaos and time-series analysis (2003), Oxford University Press, p. 116-7 · Zbl 1012.37001 |
| [19] | Rosenstein, M. T.; Collins, J. J.; De Luca, C. J., A practical method for calculating largest Lyapunov exponents from small data sets, Physica D, 65, 117-134 (1993) · Zbl 0779.58030 |
| [20] | Hasting, A., Complex interactions between dispersal and dynamics: lessons from coupled logistic equations, Ecology, 74, 1362-1372 (1993) |
| [21] | Xu, C. L.; Li, Z. Z., Effects of diffusion and spatially varying predation risk on the dynamics and equilibrium density of a predator-prey system, J Theor Biol, 219, 73-82 (2002) |
| [22] | Kaitala, V.; Ranta, E., Red/blue chaotic power spectra, Nature, 381, 198-199 (1996) |
| [23] | Gakkhar, S.; Naji, R. K., Chaos in seasonally perturbed ratio-dependent prey-predator system, Chaos Solitons & Fractals, 15, 107-118 (2003) · Zbl 1033.92026 |
| [24] | Hanski, I.; Turchin, P.; Korpimaki, E.; Henttonen, H., Population oscillations of boreal rodents:regulation by mustelid predators lead to chaos, Nature, 364, 232-235 (1993) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
