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Discrete Dynamics in Nature and Society
Volume 2014 (2014), Article ID 402194, 10 pages
Dynamical Analysis of a Plateau Pika with Cross-Diffusion under Contraception Control
1School of Information and Communication Engineering, North University of China, Shanxi, Taiyuan 030051, China
2Department of Applied Mathematics, Yuncheng University, Shanxi, Yuncheng 044000, China
Received 6 July 2013; Revised 25 December 2013; Accepted 26 December 2013; Published 18 February 2014
Academic Editor: Seenith Sivasundaram
Copyright © 2014 Xiaoyan Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- A. T. Smith and J. M. Foggin, “The plateau pika (Ochotona curzoniae) is a keystone species for biodiversity on the Tibetan plateau,” Animal Conservation, vol. 2, no. 4, pp. 235–240, 1999.
- C. H. Lai and A. T. Smith, “Keystone status of plateau pikas (Ochotona curzoniae): effect of control on biodiversity of native birds,” Biodiversity and Conservation, vol. 12, no. 9, pp. 1901–1912, 2003.
- C. Wang, H. He, M. Li et al., “Parasite species associated with wild plateau pika (Ochotona curzoniae) in southeastern Qinghai Province, China,” Journal of Wildlife Diseases, vol. 45, no. 2, pp. 288–294, 2009.
- Z. L. Wang, Y. Chen, J. Yang, W. J. Chen, Y. M. Zhang, and X. Q. Zhao, “Behavioral mechanisms of male sterilization on plateau pika in the Qinghai-Tibet plateau,” Behavioural Processes, vol. 89, no. 3, pp. 278–285, 2012.
- F. S. Dobson, A. T. Smith, and W. X. Gao, “The mating system and gene dynamics of plateau pikas,” Behavioural Processes, vol. 51, no. 1–3, pp. 101–110, 2000.
- G. C. Smith and C. L. Cheeseman, “A mathematical model for the control of diseases in wildlife populations: culling, vaccination and fertility control,” Ecological Modelling, vol. 150, no. 1-2, pp. 45–53, 2002.
- T. V. Burkey and N. C. Stenseth, “Population dynamics of territorial species in seasonal and patchy environments,” Oikos, vol. 69, no. 1, pp. 47–53, 1994.
- H. W. Liu, Z. Jin, Y. M. Chen, and F. Q. Zhang, “Population dynamics of plateau pika under lethalcontrol and contraception control,” Advances in Difference Equations, vol. 2012, article 29, 13 pages, 2012.
- H. W. Liu and Q. Y. Li, “Model of single-species population under contraceptive control and lethal control,” Mathematics in Practice and Theory, vol. 39, no. 15, pp. 104–107, 2009.
- H. W. Liu, L. Zhou, W. Liu, and H. K. Zhou, “Using a cellular-automata model to investigate the effects of grazing on plateau pika population dynamics,” International Journal of Biomathematics, vol. 4, no. 3, pp. 275–287, 2011.
- M. Z. Jessie and S. H. David, “Polygynandry and even-sexed dispersal in a population of collared pikas, Ochotona collaris,” Animal Behaviour, vol. 83, no. 4, pp. 1075–1082, 2012.
- F. S. Dobson, A. T. Smith, and W. X. Gao, “Social and ecological influences on dispersal and philopatry in the plateau pika,” Behavioral Ecology, vol. 9, no. 6, pp. 622–635, 1998.
- Y.-X. Wang and W.-T. Li, “Effects of cross-diffusion and heterogeneous environment on positive steady states of a prey-predator system,” Nonlinear Analysis: Real World Applications, vol. 14, no. 2, pp. 1235–1246, 2013.
- Y.-X. Wang and W.-T. Li, “Effect of cross-diffusion on the stationary problem of a diffusive competition model with a protection zone,” Nonlinear Analysis: Real World Applications, vol. 14, no. 1, pp. 224–245, 2013.
- P. Y. H. Pang and M. X. Wang, “Existence of global solutions for a three-species predator-prey model with cross-diffusion,” Mathematische Nachrichten, vol. 281, no. 4, pp. 555–560, 2008.
- J. Liu, H. Zhou, and L. Zhang, “Cross-diffusion induced Turing patterns in a sex-structured predator-prey model,” International Journal of Biomathematics, vol. 5, no. 4, Article ID 1250016, 23 pages, 2012.
- G.-P. Hu and X.-L. Li, “Turing patterns of a predator-prey model with a modified Leslie-Gower term and cross-diffusions,” International Journal of Biomathematics, vol. 5, no. 6, Article ID 1250060, 17 pages, 2012.
- C. R. Tian, Z. G. Lin, and M. Pedersen, “Instability induced by cross-diffusion in reaction-diffusion systems,” Nonlinear Analysis: Real World Applications, vol. 11, no. 2, pp. 1036–1045, 2010.
- G. Gambino, M. C. Lombardo, and M. Sammartino, “Turing instability and traveling fronts for a nonlinear reaction-diffusion system with cross-diffusion,” Mathematics and Computers in Simulation, vol. 82, no. 6, pp. 1112–1132, 2012.
- Z. Xie, “Cross-diffusion induced Turing instability for a three species food chain model,” Journal of Mathematical Analysis and Applications, vol. 388, no. 1, pp. 539–547, 2012.
- R. Ruiz-Baier and C. Tian, “Mathematical analysis and numerical simulation of pattern formation under cross-diffusion,” Nonlinear Analysis: Real World Applications, vol. 14, no. 1, pp. 601–612, 2013.
- W. Ko and K. Ryu, “On a predator-prey system with cross diffusion representing the tendency of predators in the presence of prey species,” Journal of Mathematical Analysis and Applications, vol. 341, no. 2, pp. 1133–1142, 2008.
- W.-M. Ni, “Diffusion, cross-diffusion, and their spike-layer steady states,” Notices of the American Mathematical Society, vol. 45, no. 1, pp. 9–18, 1998.
- T. Kolokolnikov and J. Wei, “Stability of spiky solutions in a competition model with cross-diffusion,” SIAM Journal on Applied Mathematics, vol. 71, no. 4, pp. 1428–1457, 2011.
- Y. Lou and W. M. Ni, “Diffusion, self-diffusion and cross-diffusion,” Journal of Differential Equations, vol. 131, no. 1, pp. 79–131, 1996.
- Y. Lou and W.-M. Ni, “Diffusion vs cross-diffusion: an elliptic approach,” Journal of Differential Equations, vol. 154, no. 1, pp. 157–190, 1999.
- Y. Lou, W.-M. Ni, and Y. Wu, “On the global existence of a cross-diffusion system,” Discrete and Continuous Dynamical Systems, vol. 4, no. 2, pp. 193–203, 1998.
- P. V. Tuôc, “Global existence of solutions to Shigesada-Kawasaki-Teramoto cross-diffusion systems on domains of arbitrary dimensions,” Proceedings of the American Mathematical Society, vol. 135, no. 12, pp. 3933–3941, 2007.
- X. Zeng, “Non-constant positive steady states of a prey-predator system with cross-diffusions,” Journal of Mathematical Analysis and Applications, vol. 332, no. 2, pp. 989–1009, 2007.
- L. S. Lin, W. M. Ni, and I. Takagi, “Large amplitude stationary solutions to a chemotaxis system,” Journal of Differential Equations, vol. 72, no. 1, pp. 1–27, 1988.