# American Institute of Mathematical Sciences

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

 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.
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] 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 [4] 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 [5] 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 [6] 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 [7] 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 [8] 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 [9] 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 [10] 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 [11] 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 [12] Reza Lotfi, Gerhard-Wilhelm Weber, S. Mehdi Sajadifar, Nooshin Mardani. Interdependent demand in the two-period newsvendor problem. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-24. doi: 10.3934/jimo.2018143 [13] 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 [14] 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 [15] 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 [16] 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 [17] G. Chen, C. Li, C. Liu, Jaume Llibre. The cyclicity of period annuli of some classes of reversible quadratic systems. Discrete & Continuous Dynamical Systems - A, 2006, 16 (1) : 157-177. doi: 10.3934/dcds.2006.16.157 [18] Àngel Jorba, Pau Rabassa, Joan Carles Tatjer. Period doubling and reducibility in the quasi-periodically forced logistic map. Discrete & Continuous Dynamical Systems - B, 2012, 17 (5) : 1507-1535. doi: 10.3934/dcdsb.2012.17.1507 [19] Long Zhang, Gao Xu, Zhidong Teng. Intermittent dispersal population model with almost period parameters and dispersal delays. Discrete & Continuous Dynamical Systems - B, 2016, 21 (6) : 2011-2037. doi: 10.3934/dcdsb.2016034 [20] Zhiting Xu, Xiao-Qiang Zhao. A vector-bias malaria model with incubation period and diffusion. Discrete & Continuous Dynamical Systems - B, 2012, 17 (7) : 2615-2634. doi: 10.3934/dcdsb.2012.17.2615

2018 Impact Factor: 1.313