Dynamics of a periodically switched predator-prey model with seasonal birth, predation-induced fear, intraspecific cooperative hunting and predator migrating for chasing foods

Hui Jiao; Akanat Wetayawanich; Jianjun Jiao; Hui Jiao; Akanat Wetayawanich; Jianjun Jiao

doi:10.3934/math.20261296

AIMS Mathematics

2026, Volume 11, Issue 10: 33045-33069. doi: 10.3934/math.20261296

Previous Article Next Article

Research article

Dynamics of a periodically switched predator-prey model with seasonal birth, predation-induced fear, intraspecific cooperative hunting and predator migrating for chasing foods

1.
School of Mathematics and Geoinformations, Institute of Science, Suranaree University of Technology, Nakhon, Ratchasima 30000, Thailand
2.
School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550004, China

Received: 17 July 2026 Revised: 11 September 2026 Accepted: 23 September 2026 Published: 12 October 2026
MSC : 34A37, 92D25

In view of seasonal birth, predation-induced fear, intraspecific cooperative hunting, and predator migrating for chasing foods, we constructed a new periodically switched predator-prey model for ecological protection. Exploiting theories of impulsive differential equations, we obtained the sufficient conditions for system persistence and the prey-eradication boundary periodic solution being globally asymptotically stable. Bifurcation analysis was used to reveal rich dynamical properties of system $ (2.1) $ with numerical simulations, including the periodic solution, period-doubling solutions, and chaos. We also found that the fear effect, intraspecific cooperative hunting, and predator seasonal migration have significant impacts on the persistence of system (2.1).
- periodically switched predator-prey model,
- seasonally migrating for chasing food,
- intraspecific cooperative hunting,
- fear effect,
- persistence
Citation: Hui Jiao, Akanat Wetayawanich, Jianjun Jiao. Dynamics of a periodically switched predator-prey model with seasonal birth, predation-induced fear, intraspecific cooperative hunting and predator migrating for chasing foods[J]. AIMS Mathematics, 2026, 11(10): 33045-33069. doi: 10.3934/math.20261296

Related Papers:

Abstract

In view of seasonal birth, predation-induced fear, intraspecific cooperative hunting, and predator migrating for chasing foods, we constructed a new periodically switched predator-prey model for ecological protection. Exploiting theories of impulsive differential equations, we obtained the sufficient conditions for system persistence and the prey-eradication boundary periodic solution being globally asymptotically stable. Bifurcation analysis was used to reveal rich dynamical properties of system $ (2.1) $ with numerical simulations, including the periodic solution, period-doubling solutions, and chaos. We also found that the fear effect, intraspecific cooperative hunting, and predator seasonal migration have significant impacts on the persistence of system (2.1).

References

[1]	K. A. Hobson, L. I. Wassenaar, Tracking animal migration with stable isotopes, London: Academic Press, 2019. https://doi.org/10.1016/C2017-0-01125-4
[2]	Y. Cheng, Z. Wen, X. He, Z. Dong, M. Zhangshang, D. Li, et al., Ecological traits affect the seasonal migration patterns of breeding birds along a subtropical altitudinal gradient, Avian Res., 13 (2022), 100066. https://doi.org/10.1016/j.avrs.2022.100066 doi: 10.1016/j.avrs.2022.100066
[3]	Y. Liao, T. Zhao, W. Du, D. Wang, Z. Peng, S. Xue, et al., How virus migration and meteorological elements shape the seasonality of influenza A/H3N2: a case study in China, One Health, 20 (2025), 101037. https://doi.org/10.1016/j.onehlt.2025.101037 doi: 10.1016/j.onehlt.2025.101037
[4]	J. Zhang, P. Y. Tishchenko, Z. J. Jiang, P. Y. Semkin, P. P. Tishchenko, W. Zheng, et al., Diverse nature of the seasonally coastal eutrophication dominated by oceanic nutrients: an eco-system based analysis characterized by salmon migration and aquaculture, Mar. Pollut. Bull., 193 (2023), 115150. https://doi.org/10.1016/j.marpolbul.2023.115150 doi: 10.1016/j.marpolbul.2023.115150
[5]	J. Jiao, S. Cai, L. Li, Impulsive vaccination and dispersal on dynamics of an SIR epidemic model with restricting infected individuals boarding transports, Physica A, 449 (2016), 145–159. https://doi.org/10.1016/j.physa.2015.10.055 doi: 10.1016/j.physa.2015.10.055
[6]	J. Jiao, Y. Xiao, Dynamics of a pest-natural enemy model with natural enemy periodic migration described by time delay, Nonlinear Anal. Real World Appl., 87 (2026), 104454. https://doi.org/10.1016/j.nonrwa.2025.104454 doi: 10.1016/j.nonrwa.2025.104454
[7]	J. Jiao, Q. Quan, X. Dai, Dynamics of a new impulsive predator-prey model with predator population seasonally large-scale migration, Appl. Math. Lett., 132 (2022), 108096. https://doi.org/10.1016/j.aml.2022.108096 doi: 10.1016/j.aml.2022.108096
[8]	S. Creel, B. Goodheart, J. R. de Merkle, J. Redcliffe, H. Mwape, S. Matsushima, et al., Prey depletion and the effect of group size on cooperative hunting in African wild dogs, Anim. Behav., 234 (2026), 123504. https://doi.org/10.1016/j.anbehav.2026.123504 doi: 10.1016/j.anbehav.2026.123504
[9]	Shivam, K. Singh, M. Kumar, R. Dubey, T. Singh, Untangling role of cooperative hunting among predators and herd behavior in prey with a dynamical systems approach, Chaos Soliton Fract., 162 (2022), 112420. https://doi.org/10.1016/j.chaos.2022.112420 doi: 10.1016/j.chaos.2022.112420
[10]	Y. Mu, W. C. Lo, Y. S. Tan, Z. J. Liu, Hybrid control for the prey in a spatial prey-predator model with cooperative hunting and fear effect time lag, Appl. Math. Comput., 491 (2025), 129217. https://doi.org/10.1016/j.amc.2024.129217 doi: 10.1016/j.amc.2024.129217
[11]	J. A. Vucetich, R. O. Peterson, T. A. Waite, Raven scavenging favours group foraging in wolves, Anim. Behav., 67 (2004), 1117–1126. https://doi.org/10.1016/j.anbehav.2003.06.018 doi: 10.1016/j.anbehav.2003.06.018
[12]	S. Creel, N. M. Creel, Communal hunting and pack size in African wild dogs, Lycaon pictus, Anim. Behav., 50 (1995), 1325–1339. https://doi.org/10.1016/0003-3472(95)80048-4 doi: 10.1016/0003-3472(95)80048-4
[13]	L. Wu, J. Jiao, Q. Quan, H. Sun, Dynamics of a pest management model with nonlinearly impulsive releasing two types of natural enemies and their interspecific cooperation, Chaos Solitons Fract., 199 (2025), 116805. https://doi.org/10.1016/j.chaos.2025.116805 doi: 10.1016/j.chaos.2025.116805
[14]	H. Jiao, Dynamics of a switched pest management model with seasonally migrating, predation-induced fear and unilaterally interspecific cooperative hunting, Int. J. Biomath., (2025), 2550118. https://doi.org/10.1142/S1793524525501189
[15]	S. Banerjee, A. Sha, J. Chattopadhyay, Cooperative predation on mutualistic prey communities, J. Theor. Biol., 490 (2020), 110156. https://doi.org/10.1016/j.jtbi.2020.110156 doi: 10.1016/j.jtbi.2020.110156
[16]	X. Wang, L. Zanette, X. Zou, Modelling the fear effect in predator-prey interactions, J. Math. Biol., 73 (2016), 1179–1204. https://doi.org/10.1007/s00285-016-0989-1 doi: 10.1007/s00285-016-0989-1
[17]	M. Hossain, N. Pal, S. Samanta, Impact of fear on an eco-epidemiological model, Chaos Solitons Fract., 134 (2020), 109718. https://doi.org/10.1016/j.chaos.2020.109718 doi: 10.1016/j.chaos.2020.109718
[18]	W. Cresswell, J. L. Quinn, Predicting the optimal prey group size from predator hunting behaviour, J. Anim. Ecol., 80 (2011), 310–319. https://doi.org/10.1111/j.1365-2656.2010.01775.x doi: 10.1111/j.1365-2656.2010.01775.x
[19]	J. S. Brown, J. W. Laundre, M. Gurung, The ecology of fear: optimal foraging, game theory and trophic interactions, J. Mammal., 80 (1999), 385–399. https://doi.org/10.2307/1383287 doi: 10.2307/1383287
[20]	L. Y. Zanette, A. F. White, M. C. Allen, M. Clinchy, Perceived predation risk reduces the number of offspring songbirds produce per year, Science, 334 (2011), 1398–1401. https://doi.org/10.1126/science.1210908 doi: 10.1126/science.1210908
[21]	R. Shi, Analysis of plankton-fish system with delay of fear effect, Phys. Lett. A, 551 (2025), 130583. https://doi.org/10.1016/j.physleta.2025.130583 doi: 10.1016/j.physleta.2025.130583
[22]	S. Saha, S. Pal, V. Melnik, Analysis of the impact of fear in the presence of additional food and prey refuge with nonlocal predator-prey models, Ecol. Model., 505 (2025), 111103. https://doi.org/10.1016/j.ecolmodel.2025.111103 doi: 10.1016/j.ecolmodel.2025.111103
[23]	V. Kumar, S. K. Bairwa, Tanvi, Influence of fear and Allee effects on stability and species survival in a tri-trophic food chain, Commun. Nonlinear Sci. Numer. Simul., 152 (2026), 109115. https://doi.org/10.1016/j.cnsns.2025.109115 doi: 10.1016/j.cnsns.2025.109115
[24]	H. Sun, J. Jiao, L. Wu, Dynamics of a periodic switched pest management model under the influence of fear effect, J. Math. Anal. Appl., 553 (2026), 129860. https://doi.org/10.1016/j.jmaa.2025.129860 doi: 10.1016/j.jmaa.2025.129860
[25]	S. A. Levin, Dispersion and population interactions, Am. Nat., 108 (1974), 207–228. https://doi.org/10.1086/282900 doi: 10.1086/282900
[26]	L. Xiong, K. Wu, Limit cycles for continuous piecewise linear systems with three zones having two degenerate subsystems, J. Math. Interdiscip. Appl., 1 (2025), 3–19. https://doi.org/10.62762/JMIA.2025.453419 doi: 10.62762/JMIA.2025.453419
[27]	B. Chang, Y. Tan, A stochastic impulsive competition model for tumor evolution under intermittent androgen deprivation therapy, J. Math. Interdiscip. Appl., 2 (2026), 36–53. https://doi.org/10.62762/JMIA.2025.355794 doi: 10.62762/JMIA.2025.355794
[28]	J. Jiao, Z. Liu, S. Cai, Dynamics of an SEIR model with infectivity in incubation period and homestead-isolation on the susceptible, Appl. Math. Lett., 107 (2020), 106442. https://doi.org/10.1016/j.aml.2020.106442 doi: 10.1016/j.aml.2020.106442
[29]	L. Chen, X. Meng, J. Jiao, Biological dynamics (in Chinese), Beijing: Scientific Press, 2009.
[30]	V. Lakshmikantham, D. D. Bainov, P. S. Simeonov, Theory of impulsive differential equations, Singapore: World Scientific, 1989. https://doi.org/10.1142/0906
[31]	H. Jiao, S. Meleshko, Analysis of a pest-natural enemy model with time delay in impulsive releasing natural enemy, J. Math. Interdiscip. Appl., 1 (2025), 20–28. https://doi.org/10.62762/JMIA.2025.442174 doi: 10.62762/JMIA.2025.442174
[32]	J. Jiao, S. Cai, L. Li, Dynamics of a periodic switched predator-prey system with impulsive harvesting and hibernation of prey population, J. Franklin Inst., 353 (2016), 3818–3834. https://doi.org/10.1016/j.jfranklin.2016.06.035 doi: 10.1016/j.jfranklin.2016.06.035
[33]	X. Liu, L. Chen, Complex dynamics of Holling type Ⅱ Lotka-Volterra predator-prey system with impulsive perturbations on the predator, Chaos Solitons Fract., 16 (2003), 311–320. https://doi.org/10.1016/S0960-0779(02)00408-3 doi: 10.1016/S0960-0779(02)00408-3
[34]	J. Jiao, S. Cai, L. Chen, Analysis of a stage-structured predator-prey system with birth pulse and impulsive harvesting at different moments, Nonlinear Anal. Real World Appl., 12 (2011), 2232–2244. https://doi.org/10.1016/j.nonrwa.2011.01.005 doi: 10.1016/j.nonrwa.2011.01.005
[35]	J. Jiao, Y. Xiao, H. Jiao, Dynamics of a switched predator-prey breeding management model with impulsive nonlinear releasing and age-selective harvesting predator, Adv. Contin. Discret. M., 2025 (2025), 101. https://doi.org/10.1186/s13662-025-03960-6 doi: 10.1186/s13662-025-03960-6
[36]	H. J. Alsakaji, S. Kundu, F. A. Rihan, Delay differential model of one-predator two-prey system with Monod-Haldane and Holling type Ⅱ functional responses, Appl. Math. Comput., 397 (2021), 125919. https://doi.org/10.1016/j.amc.2020.125919 doi: 10.1016/j.amc.2020.125919
[37]	F. A. Rihan, H. J. Alsakaji, Persistence and extinction for stochastic delay differential model of prey predator system with hunting cooperation in predators, Adv. Differ. Equ., 2020 (2020), 124. https://doi.org/10.1186/s13662-020-02579-z doi: 10.1186/s13662-020-02579-z
[38]	Y. Wang, X. Meng, Strategy dynamics of three-strategy snowdrift game induced by reward strategy and payoff delay, J. Math. Interdiscip. Appl., 2 (2026), 74–90. https://doi.org/10.62762/JMIA.2026.346326 doi: 10.62762/JMIA.2026.346326

Reader Comments

Your name:*

Email:*
© 2026 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)