Pattern formation in a ratio-dependent predator-prey model with cross-diffusion
Author
Abstract
Suggested Citation
DOI: 10.1016/j.amc.2018.03.033
Download full text from publisher
As the access to this document is restricted, you may want to search for a different version of it.
References listed on IDEAS
- Camara, B.I. & Haque, M. & Mokrani, H., 2016. "Patterns formations in a diffusive ratio-dependent predator–prey model of interacting populations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 374-383.
- Tian, Canrong & Ling, Zhi & Zhang, Lai, 2017. "Nonlocal interaction driven pattern formation in a prey–predator model," Applied Mathematics and Computation, Elsevier, vol. 308(C), pages 73-83.
- Hezi Yizhaq & Boris A Portnov & Ehud Meron, 2004. "A Mathematical Model of Segregation Patterns in Residential Neighbourhoods," Environment and Planning A, , vol. 36(1), pages 149-172, January.
- Peng, Yahong & Zhang, Tonghua, 2016. "Turing instability and pattern induced by cross-diffusion in a predator-prey system with Allee effect," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 1-12.
Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
Cited by:
- Meng Zhu & Jing Li & Xinze Lian, 2022. "Pattern Dynamics of Cross Diffusion Predator–Prey System with Strong Allee Effect and Hunting Cooperation," Mathematics, MDPI, vol. 10(17), pages 1-20, September.
- Peng, Yahong & Zhang, Guoying, 2020. "Dynamics analysis of a predator–prey model with herd behavior and nonlocal prey competition," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 170(C), pages 366-378.
- Mohan, Nishith & Kumari, Nitu, 2021. "Positive steady states of a SI epidemic model with cross diffusion," Applied Mathematics and Computation, Elsevier, vol. 410(C).
- Sajan, & Anshu, & Dubey, Balram, 2024. "Study of a cannibalistic prey–predator model with Allee effect in prey under the presence of diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
- Yangyang Shao & Yan Meng & Xinyue Xu, 2022. "Turing Instability and Spatiotemporal Pattern Formation Induced by Nonlinear Reaction Cross-Diffusion in a Predator–Prey System with Allee Effect," Mathematics, MDPI, vol. 10(9), pages 1-15, May.
- Souna, Fethi & Belabbas, Mustapha & Menacer, Youssaf, 2023. "Complex pattern formations induced by the presence of cross-diffusion in a generalized predator–prey model incorporating the Holling type functional response and generalization of habitat complexity e," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 597-618.
- Wang, Henan & Liu, Ping, 2023. "Pattern dynamics of a predator–prey system with cross-diffusion, Allee effect and generalized Holling IV functional response," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
- Chakraborty, Bhaskar & Ghorai, Santu & Bairagi, Nandadulal, 2020. "Reaction-diffusion predator-prey-parasite system and spatiotemporal complexity," Applied Mathematics and Computation, Elsevier, vol. 386(C).
Most related items
These are the items that most often cite the same works as this one and are cited by the same works as this one.- Li, Qiang & Liu, Zhijun & Yuan, Sanling, 2019. "Cross-diffusion induced Turing instability for a competition model with saturation effect," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 64-77.
- Hua Liu & Yong Ye & Yumei Wei & Weiyuan Ma & Ming Ma & Kai Zhang, 2019. "Pattern Formation in a Reaction-Diffusion Predator-Prey Model with Weak Allee Effect and Delay," Complexity, Hindawi, vol. 2019, pages 1-14, November.
- Liu, Yanwei & Zhang, Tonghua & Liu, Xia, 2020. "Investigating the interactions between Allee effect and harvesting behaviour of a single species model: An evolutionary dynamics approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
- Huang, Tousheng & Yang, Hongju & Zhang, Huayong & Cong, Xuebing & Pan, Ge, 2018. "Diverse self-organized patterns and complex pattern transitions in a discrete ratio-dependent predator–prey system," Applied Mathematics and Computation, Elsevier, vol. 326(C), pages 141-158.
- Wu, Daiyong & Zhao, Min, 2019. "Qualitative analysis for a diffusive predator–prey model with hunting cooperative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 299-309.
- Wang, Fatao & Yang, Ruizhi & Zhang, Xin, 2024. "Turing patterns in a predator–prey model with double Allee effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 170-191.
- Aybar, I. Kusbeyzi & Aybar, O.O. & Dukarić, M. & Ferčec, B., 2018. "Dynamical analysis of a two prey-one predator system with quadratic self interaction," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 118-132.
- Zhang, Feifan & Sun, Jiamin & Tian, Wang, 2022. "Spatiotemporal pattern selection in a nontoxic-phytoplankton - toxic-phytoplankton - zooplankton model with toxin avoidance effects," Applied Mathematics and Computation, Elsevier, vol. 423(C).
- Yan, Shuixian & Jia, Dongxue & Zhang, Tonghua & Yuan, Sanling, 2020. "Pattern dynamics in a diffusive predator-prey model with hunting cooperations," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
- Zhou, Weigang & Huang, Chengdai & Xiao, Min & Cao, Jinde, 2019. "Hybrid tactics for bifurcation control in a fractional-order delayed predator–prey model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 183-191.
- Mandal, Sayan & Sk, Nazmul & Tiwari, Pankaj Kumar & Chattopadhyay, Joydev, 2024. "Bistability in modified Holling II response model with harvesting and Allee effect: Exploring transitions in a noisy environment," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
- Wu, Zeyan & Li, Jianjuan & Liu, Shuying & Zhou, Liuting & Luo, Yang, 2019. "A spatial predator–prey system with non-renewable resources," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 381-391.
- Kalyan Manna & Vitaly Volpert & Malay Banerjee, 2020. "Dynamics of a Diffusive Two-Prey-One-Predator Model with Nonlocal Intra-Specific Competition for Both the Prey Species," Mathematics, MDPI, vol. 8(1), pages 1-28, January.
- Guo, Gaihui & Qin, Qijing & Cao, Hui & Jia, Yunfeng & Pang, Danfeng, 2024. "Pattern formation of a spatial vegetation system with cross-diffusion and nonlocal delay," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
- Ghorai, Santu & Chakraborty, Bhaskar & Bairagi, Nandadulal, 2021. "Preferential selection of zooplankton and emergence of spatiotemporal patterns in plankton population," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
- Shivam, & Singh, Kuldeep & Kumar, Mukesh & Dubey, Ramu & Singh, Teekam, 2022. "Untangling role of cooperative hunting among predators and herd behavior in prey with a dynamical systems approach," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
- Gambino, G. & Lombardo, M.C. & Sammartino, M., 2012. "Turing instability and traveling fronts for a nonlinear reaction–diffusion system with cross-diffusion," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(6), pages 1112-1132.
- Tang, Xiaosong & Zhang, Xiaoyu & Liu, Yiting & Li, Wankun & Zhong, Qi, 2023. "Global stability and Turing instability deduced by cross-diffusion in a delayed diffusive cooperative species model," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
- Saifuddin, Md. & Biswas, Santanu & Samanta, Sudip & Sarkar, Susmita & Chattopadhyay, Joydev, 2016. "Complex dynamics of an eco-epidemiological model with different competition coefficients and weak Allee in the predator," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 270-285.
- Chen, Mengxin & Wu, Ranchao & Chen, Liping, 2020. "Spatiotemporal patterns induced by Turing and Turing-Hopf bifurcations in a predator-prey system," Applied Mathematics and Computation, Elsevier, vol. 380(C).
More about this item
Keywords
Predator-prey model; Cross-diffusion; Turing instability; Amplitude equations; Pattern formation;All these keywords.
Statistics
Access and download statisticsCorrections
All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:331:y:2018:i:c:p:307-318. See general information about how to correct material in RePEc.
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .
Please note that corrections may take a couple of weeks to filter through the various RePEc services.