American Institute of Mathematical Sciences

Advanced
2010, 7(2): 443-453. doi: 10.3934/mbe.2010.7.443

Mathematical observations on the relation between eclosion periods and the copulation rate of cicadas

Yasumasa Saisho 1,

1. 

Department of Applied Mathematics, Graduate School of Engineering, Hiroshima University, Kagamiyama 1-4-1, Higashi-hiroshima, 739-8527, Japan

Received  January 2009 Revised  November 2009 Published  April 2010

In many species of cicadas the peak of eclosion of males precedes that of females. In this paper, we construct a stochastic model and consider whether this sexual difference of eclosion periods works against mating or not. We also discuss the relation between the peak period of copulations and the development of population number by using this model.
Keywords: copulation rate, cicada, eclosion period, peak period of copulations..
Mathematics Subject Classification: 65C20, 65C5.
Citation: Yasumasa Saisho. Mathematical observations on the relation between eclosion periods and the copulation rate of cicadas. Mathematical Biosciences & Engineering, 2010, 7 (2) : 443-453. doi: 10.3934/mbe.2010.7.443
[1]

Yu Yang, Dongmei Xiao. Influence of latent period and nonlinear incidence rate on the dynamics of SIRS epidemiological models. Discrete & Continuous Dynamical Systems - B, 2010, 13 (1) : 195-211. doi: 10.3934/dcdsb.2010.13.195
[2]

Peter Seibt. A period formula for torus automorphisms. Discrete & Continuous Dynamical Systems - A, 2003, 9 (4) : 1029-1048. doi: 10.3934/dcds.2003.9.1029
[3]

Lihua Bian, Zhongfei Li, Haixiang Yao. Time-consistent strategy for a multi-period mean-variance asset-liability management problem with stochastic interest rate. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020026
[4]

Kaijen Cheng, Kenneth Palmer, Yuh-Jenn Wu. Period 3 and chaos for unimodal maps. Discrete & Continuous Dynamical Systems - A, 2014, 34 (5) : 1933-1949. doi: 10.3934/dcds.2014.34.1933
[5]

Ely Kerman. On primes and period growth for Hamiltonian diffeomorphisms. Journal of Modern Dynamics, 2012, 6 (1) : 41-58. doi: 10.3934/jmd.2012.6.41
[6]

Yulin Zhao. On the monotonicity of the period function of a quadratic system. Discrete & Continuous Dynamical Systems - A, 2005, 13 (3) : 795-810. doi: 10.3934/dcds.2005.13.795
[7]

Reza Lotfi, Gerhard-Wilhelm Weber, S. Mehdi Sajadifar, Nooshin Mardani. Interdependent demand in the two-period newsvendor problem. Journal of Industrial & Management Optimization, 2020, 16 (1) : 117-140. doi: 10.3934/jimo.2018143
[8]

Yukihiko Nakata. Existence of a period two solution of a delay differential equation. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020392
[9]

Linping Peng, Yazhi Lei. The cyclicity of the period annulus of a quadratic reversible system with a hemicycle. Discrete & Continuous Dynamical Systems - A, 2011, 30 (3) : 873-890. doi: 10.3934/dcds.2011.30.873
[10]

Guibin Lu, Qiying Hu, Youying Zhou, Wuyi Yue. Optimal execution strategy with an endogenously determined sales period. Journal of Industrial & Management Optimization, 2005, 1 (3) : 289-304. doi: 10.3934/jimo.2005.1.289
[11]

Yi Shao, Yulin Zhao. The cyclicity of the period annulus of a class of quadratic reversible system. Communications on Pure & Applied Analysis, 2012, 11 (3) : 1269-1283. doi: 10.3934/cpaa.2012.11.1269
[12]

Marcelo Marchesin. The mass dependence of the period of the periodic solutions of the Sitnikov problem. Discrete & Continuous Dynamical Systems - S, 2008, 1 (4) : 597-609. doi: 10.3934/dcdss.2008.1.597
[13]

Adriana Buică, Jaume Giné, Maite Grau. Essential perturbations of polynomial vector fields with a period annulus. Communications on Pure & Applied Analysis, 2015, 14 (3) : 1073-1095. doi: 10.3934/cpaa.2015.14.1073
[14]

James W. Cannon, Mark H. Meilstrup, Andreas Zastrow. The period set of a map from the Cantor set to itself. Discrete & Continuous Dynamical Systems - A, 2013, 33 (7) : 2667-2679. doi: 10.3934/dcds.2013.33.2667
[15]

Kebing Chen, Haijie Zhou, Dong Lei. Two-period pricing and ordering decisions of perishable products with a learning period for demand disruption. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020111
[16]

Denis Dmitriev, Jonathan Jedwab. Bounds on the growth rate of the peak sidelobe level of binary sequences. Advances in Mathematics of Communications, 2007, 1 (4) : 461-475. doi: 10.3934/amc.2007.1.461
[17]

Edoardo Beretta, Dimitri Breda. An SEIR epidemic model with constant latency time and infectious period. Mathematical Biosciences & Engineering, 2011, 8 (4) : 931-952. doi: 10.3934/mbe.2011.8.931
[18]

Lin Jiang, Song Wang. Robust multi-period and multi-objective portfolio selection. Journal of Industrial & Management Optimization, 2019  doi: 10.3934/jimo.2019130
[19]

Brandy Rapatski, Petra Klepac, Stephen Dueck, Maoxing Liu, Leda Ivic Weiss. Mathematical epidemiology of HIV/AIDS in cuba during the period 1986-2000. Mathematical Biosciences & Engineering, 2006, 3 (3) : 545-556. doi: 10.3934/mbe.2006.3.545
[20]

Alexander O. Brown, Christopher S. Tang. The impact of alternative performance measures on single-period inventory policy. Journal of Industrial & Management Optimization, 2006, 2 (3) : 297-318. doi: 10.3934/jimo.2006.2.297

2018 Impact Factor: 1.313

Tools

Metrics

  • PDF downloads (20)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences