Investigation of an Interacting Fractional-Order Predator–Prey System in Presence of Fear and Harvesting

Iranian Journal of Science - Tập 47 Số 5-6 - Trang 1739-1749 - 2023
Sunil Kumar1,2, Ravikant Singh3, R.P. Chauhan4, Nilesh Kumar Thakur3
1Department of Mathematics, College of Science, King Saud University, Riyadh, Saudi Arabia
2Department of Mathematics, National Institute of Technology, Jamshedpur, India
3Department of Mathematics, National Institute of Technology, Raipur, Raipur, India
4Department of Mathematics, JECRC University, Jaipur, India

Tóm tắt

Từ khóa


Tài liệu tham khảo

Ahmed E, El-Sayed AMA, El-Saka HA (2006) On some Routh–Hurwitz conditions for fractional order differential equations and their applications in Lorenz, Rössler, Chua and Chen systems. Phys Lett A 358:1–4

Alidousti J, Ghafari E (2020) Dynamic behavior of a fractional order prey–predator model with group defense. Chaos Solitons Fractals 134:109688

Alzaid SS, Chauhan RP, Kumar S, Alkahtani BST, Alharthi MR (2022) Numerical Study for Fractional Bi-Modal 2019-nCOV SITR Epidemic Model. Fractals 30(08):2240205

Caputo M (1967) Linear models of dissipation whose Q is almost frequency independent-II. Geophys J R Astron Soc 13:529–539

Creel S, Christianson D (2008) Relationships between direct predation and risk effects. Trends Ecol Evol 23(4):194–201

Cresswell W (2011) Predation in bird populations. J Ornithol 152(1):251–263

Das M, Samanta GP (2020) A prey–predator fractional order model with fear effect and group defense. Int J Dyn Control. https://doi.org/10.1007/s40435-020-00626-x

Das M, Maiti A, Samanta GP (2018) Stability analysis of a prey–predator fractional order model incorporating prey refuge. Ecol Genet Genom 7:33–46

Elsadany AA, Matouk AE (2015) Dynamical behaviors of fractional-order Lotka–Volterra predator–prey model and its discretization. J Appl Math Comput 49:269–83

Fraker ME (2009) Predation risk assessment by green frog (Rana clamitans) tad-poles through chemical cues produced by multiple prey. Behav Ecol Sociol 63:1397–402

Ghaziani R, Alidousti J, Eshkaftaki AB (2016) Stability and dynamics of a fractional order Leslie–Gower prey–predator model. Appl Math Model 40:2075–86

Hong-LiLi Long Z, Cheng H, Yao-Lin J, Zhidong T (2016) Dynamical analysis of a fractional-order predator–prey model incorporating a prey refuge. J Appl Math Comput 54:435–49

Javidi M, Nyamoradi N (2013) Dynamic analysis of a fractional order prey–predator interaction with harvesting. Appl Math Model 37(20–21):8946–8956

Jeschke JM, Kopp M, Tollrian R (2002) Predator functional responses: discriminating between handling and digesting prey. Ecol Monogr 72:95–112

Ji G, Ge Q, Xu J (2016) Dynamic behaviors of a fractional order two-species cooperative systems with harvesting. Chaos Solitons Fract 92:51–5

Kai Diethelm, Ford Neville J (2004) Multi-order fractional differential equations and their numerical solution. Appl Math Comput 154(3):621–640

Kai Diethelm, Ford Neville J, Freed Alan D (2002) A predictor–corrector approach for the numerical solution of fractional differential equations. Nonlinear Dyn 29(1):3–22

Kai Diethelm, Ford Neville J, Freed Alan D (2004) Detailed error analysis for a fractional Adams method. Numer Algorithms 36(1):31–52

Kumar S, Chauhan RP, Aly Ayman A, Momani S, Hadid S (2022) A study on fractional HBV model through singular and non-singular derivatives. Eur Phys J Spec Top 231:1885–1904

Li Y, Chen Y, Podlubny I (2010) Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag–Leffler stability. Comput Math Appl 59:1810–1821

Li H, Jing Z, Yan CH, Li J, Zhidong T (2016) Dynamical analysis of a fractional-order predator–prey model incorporating a prey refuge. J Appl Math Comput 54:435–449

Lima SL (1998) Nonlethal effects in the ecology of predator–prey interactions. Bioscience 48(1):25–34

Lima SL (2010) Predators and the breeding bird: behavioral and reproductive flexibility under the risk of predation. Biol Rev 84(3):485–513

Maayah B, Moussaoui A, Bushnaq S, Abu Arqub O (2022a) The multistep Laplace optimized decomposition method for solving fractional-order coronavirus disease model (COVID-19) via the Caputo fractional approach. Demonstratio Mathematica 55(1):963–977

Maayah B, Arqub OA, Alnabulsi S, Alsulami H (2022b) Numerical solutions and geometric attractors of a fractional model of the cancer-immune based on the Atangana–Baleanu–Caputo derivative and the reproducing kernel scheme. Chin J Phys 80:463–483

Maji C (2022) Impact of fear effect in a fractional-order predator–prey system incorporating constant prey refuge. Nonlinear Dyn 107(1):1329–1342

Mandal M, Jana S, Nandi SK, Kar TK (2021) Modeling and analysis of a fractional-order prey–predator system incorporating harvesting. Model Earth Syst Environ 7(2):1159–1176

McCauley SJ, Rowe L, Fortin MJ (2011) The deadly effects of “nonlethal" predators. Ecology 92:2043–8

Momani S, Abu Arqub O, Maayah B (2020a) Piecewise optimal fractional reproducing kernel solution and convergence analysis for the Atangana–Baleanu–Caputo model of the Lienard’s equation. Fractals 28(8):204007

Momani S, Maayah B, Arqub OA (2020b) The reproducing kernel algorithm for numerical solution of Van der Pol damping model in view of the Atangana–Baleanu fractional approach. Fractals 28(08):2040010

Moustafa M, Mohd MH, Ismail AI (2018) Dynamical analysis of a fractional-order Rosenzweig–Macarthur model incorporating a prey refuge. Chaos Solitons Fract 109:1–13

Mukherjee D (2016) The effect of refuge and immigration in a predator–prey systems in the presence of a competitor for the prey. Nonlinear Anal Real World Appl 31:277–87

Nosrati K, Shafiee M (2017) Dynamic analysis of fractional-order singular holling type-II predator–prey system. Appl Math Comput 313:159–79

Odibat Z, Shawagfeh N (2007) Generalized Taylors formula. Appl Math Comput 186:286–293

Panday P, Pal N, Samanta S, Chattopadhyay J (2018) Stability and bifurcation analysis of a three-species food chain model with fear. Int J Bifurc Chaos 28:1850009

Panja P (2019) Dynamics of a fractional order predator–prey model with intraguild predation. Int J Simul Model 39(4):256–268

Petras I (2011) Fractional-order nonlinear system: modeling analysis and simulation. Higher Education Press, Bejing

Podlubny I (1999) Fractional differential equations. Academic Press, San Diego

Preisser EL (2009) The physiology of predator stress in free-ranging prey. J Anim Ecol 78:1103–5

Preisser EL, Bolnick DI (2008) The many faces of fear: comparing the pathways and impacts of non-consumptive predator effects on prey populations. PLoS ONE 3:e2465

Sasmal S (2018) Population dynamics with multiple Allee effects induced by fear factors induced by fear factors—a mathematical study on prey–predator. Appl Math Model 64:1–14

Siepielski AM, Wang J, Prince G (2014) Non-consumptive predator-driven mortality causes natural selection on prey. Evolution 68:696–704

Wang X, Zou X (2017) Modeling the fear effect in predator–prey interactions with adaptive avoidance of predators. Bull Math Biol 79(6):1–35

Wang X, Zanette L, Zou X (2016a) Modelling the fear effect in predator–prey interactions. J Math Biol 73:1179–204

Wang X, Zanette L, Zou X (2016b) Modelling the fear effect in predator–prey interactions. J Math Biol 73(5):1–26

Yousef A, Yousef FB (2019) Bifurcation and stability analysis of a system of fractional-order differential equations for a plant-herbivore model with Allee effect. Mathematics 7(5):454. https://doi.org/10.3390/math7050454

Yousef FB, Yousef A, Maji C (2021) Effects of fear in a fractional-order predator–prey system with predator density-dependent prey mortality. Chaos Solitons Fract 145:110711

Zanette LY, Clinchy M (2011) Perceived predation risk reduces the number of offspring songbirds produce per year. Science 334(6061):1398–1401