• Journal of the Korean Mathematical Society
• /
• v.48 no.6
• /
• pp.1225-1248
• /
• 2011

The present paper is concerned with a two-competitor/oneprey population system with Holling type-II functional response and two discrete delays. By linearizing the system at the positive equilibrium and analyzing the associated characteristic equation, the asymptotic stability of the positive equilibrium and existence of local Hopf bifurcations are investigated. Particularly, by applying the normal form theory and the center manifold reduction for functional differential equations (FDEs) explicit formulae determining the direction of bifurcations and the stability of bifurcating periodic solutions are derived. Finally, to verify our theoretical predictions, some numerical simulations are also included at the end of this paper.

• Journal of applied mathematics & informatics
• /
• v.27 no.3_4
• /
• pp.639-651
• /
• 2009

In this paper, we study a discrete Leslie-Gower one-predator two-prey model. By using the method of coincidence degree and some techniques, we obtain the existence of at least one positive periodic solution of the system. By linalization of the model at positive periodic solution and construction of Lyapunov function, sufficient conditions are obtained to ensure the global stability of the positive periodic solution. Numerical simulations are carried out to explain the analytical findings.

• Korean journal of applied entomology
• /
• v.54 no.4
• /
• pp.437-442
• /
• 2015

This study, examined Chilocorus kuwanae for biological control of Saissetia coffeae. We measured basic developmental characteristics of C. kuwanae and its capability to prey on the second-instar larvae of S. coffeae by indoor breeding under the following conditions: $25^{\circ}C{\pm}2^{\circ}C$, humidity $70%{\pm}5%$, and day length 16L : 8D. The average daily consumption of the second-instar larvae of S. coffeae by C. kuwanae adults was approximately 77.5 larvae/day, which was significantly 2.8 and 2.9 times higher than consumption by Chrysoperla carnea and Cryptolaemus montrouzieri, respectively. During the nymphal period, C. kuwanae consumed a total of 659.0 second-instar larvae of S. coffeae. The interaction between C. kuwanae and the second-instar larvae of S. coffeae varied according to their densities, with the increase in C. kuwanae consumption rate noted to decelerate and gradually level off at the maximum, rsembling Holling's Type II functional response. Duration of egg to adult development varied from 21.1 days to nearly 27.9 days at temperatures of $25^{\circ}C{\pm}2^{\circ}C$. Hatchability, pupation rate, and adult emergence were greater than 72.3%, 77.8% and 83.3%, respectively.

• Korean journal of applied entomology
• /
• v.45 no.2 s.143
• /
• pp.145-152
• /
• 2006

Predation of Neoseiulus fallacis was observed for biological control of Panonychus citri that is one of the major insect pests on citrus. The daily predation of development stages of P. citri by an adult female of N. fallacis were 20.1 eggs, 26.1 larvae, 18.2 protonymphs, and 7.4 deutonymphs at 25$^{\circ}C$, The daily predation of P. citri eggs by N, fallacis was observed under different temperatures. The predation was increased as the temperature rise. At this time, ratio of eggs production of l! fallacis after predation of P. citri eggs (number of eggs N. fallacis/number of eggs P. citri consumed by N. fallacis) was 0.09. The daily predation of P. citri eggs by N, fallacis was 21.1, 17.3, and 16.7 on the different arenas (diameter: 20, 40, and 60 mm), respectively. The predation was decreased as the arena of the leaf increase. The functional response of M fallacis to P. citri showed Holling's Type II response: the consumption of prey by N. fallacis increased as the density of prey increase but increasing rate was gradually reduced. As the result, it seemed that N. fallacis can be use for biological control of P. citri.

• Korean journal of applied entomology
• /
• v.49 no.4
• /
• pp.401-407
• /
• 2010

Daily predation of female/male O. sauteri during nymphal development were 4.2/3.9, 11.4/9.5, 14.3/10.8, and 14.7/12.5 at 17,22,27, and $32^{\circ}C$, respectively, and consumed 14.3/10.8 thrips, 7.5/7.2 aphids, 45.9/38.8 mites at $27^{\circ}C$, respectively. Adult females ate 42.8 thrips daily during preoviposition period and 63.2 thrips during oviposition period at $27^{\circ}C$. Predation by O. sauteri on F. occidentalis increased as the density of F. occidentalis increased. However, the rate of increase gradually lessened, resembling a Holling's type II functional response. The attack rate of adult female is higher than that of the 5th nymph. Adult female and 5th nymph of O. sauteri appeared to prefer 2nd larva of F. occidentalis.

• Korean journal of applied entomology
• /
• v.48 no.3
• /
• pp.347-354
• /
• 2009

This study was conducted on the biological control effects of the natural enemy, Amblyseius cucumeris, against Polyphagotarsonemus latus. The broad mite moved to a new habitat after the carrying capacity of the preferred habitat on the upper leaf has been reached. Population dynamics between predator, Amblyseius cucumeris, and prey, P. latus, were quite well synchronized since the predator followed the movement of the prey. In predation test by Amblyseius cucumeris on P. latus, A. cucumeris fed on 8.8, 15.2, 27.0 and 30.3 individuals/day under the temperatures of 15, 20, 25, and $30^{\circ}C$, respectively. The A. cucumeris larva, protonymph, deutonymph, adult male, and adult female fed on 0.5, 1.6, 5.2, 3.8, and 27 individuals of adult P. latus per day, respectively, under $25^{\circ}C$ condition. The functional response curve of adult P. latus to the densities of A. cucumeris showed Holling's Type II curve. The consumption of prey by A. cucumeris increased with the prey density increase, but the consumption rate decreased. The critical ratio of predator vs. prey effectively to suppress (98% over) the population of P. latus by releasing A. cucumeris was 1:40 on red pepper.

• Korean journal of applied entomology
• /
• v.39 no.4
• /
• pp.251-258
• /
• 2000

These studies were conducted to investigate the prey consumption and suppression of cotton aphid and green peach aphid by Chrysopa pallens Ramber as a predator. The 3$^{rd}$ instar of C. pallets fed on 29.8, 77.9, 133.6, and 155.7 individuals of apterous Aphis goussypii Glover a day at 17,22, 27, and 32$^{\circ}C$, respectively. A preovipositing female fed on 73.1 individuals, ovipositing female on 86.6 individuals, and adult male on 69.7 individuals of apterous Myzus persicae (Sulzer) a day at the 27$^{\circ}C$. The functional response curve of the larvae and adults of C. pallens to the densities of A. gossypii indicated Helling’s Type II: the consumption of prey by the C. pallens increased with the prey density but the consumption rate decreased. The attack rate of 3rd instar of C. pallens was the highest among the 2nd instar, 3$^{rd}$ instar, adult male and adult female, and handling time was the shortest. The critical ratio of the predator vs. the prey to effectively suppress the population of A. gossypii by releasing C. pallets eggs was 1 : 4 on red pepper and egg plant, and 1 : 3 on cucumber. Release of second larval stave of C. pallens at the ratio of 1 : 30 of the predator vs. the prey controlled satisfactorily A. gossypii on red pepper, and 1 : 20 on cucumber and tomato. The three-times introduction of the eggs of C. pallens was as effective as four applications of insecticides from mid-June to late September.r.