Stability Analysis and Controlling Chaos of Fractional-Order Three-Species Food Chain Model with Fear

[1]  P. Verhulst Notice sur la loi que la population pursuit dans son accroissement , 1838 .

[2]  A. Lahiri,et al.  A fractional calculus approach to Rosenzweig-MacArthur predator-prey model and its solution , 2017, 1906.01192.

[3]  I. Podlubny Fractional differential equations : an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications , 1999 .

[4]  C. S. Holling The components of prédation as revealed by a study of small-mammal prédation of the European pine sawfly. , 1959 .

[5]  Oswald J. Schmitz,et al.  Behaviorally mediated trophic cascades : Effects of predation risk on food web interactions , 1997 .

[6]  Takayuki Hanazato,et al.  Fish-induced life-history shifts in the cladocerans Daphnia and Simocephalus: are they positive or negative responses? , 2001 .

[7]  Attila Szolnoki,et al.  Cyclic dominance in evolutionary games: a review , 2014, Journal of The Royal Society Interface.

[8]  O. Agrawal,et al.  Advances in Fractional Calculus , 2007 .

[9]  J. Alidousti,et al.  Dynamical behavior of a fractional three-species food chain model , 2018, Nonlinear Dynamics.

[10]  Tonghua Zhang,et al.  Delay-induced Turing instability in reaction-diffusion equations. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  S. Peacor,et al.  Large nonlethal effects of an invasive invertebrate predator on zooplankton population growth rate. , 2007, Ecology.

[12]  R. Veit,et al.  Partial Differential Equations in Ecology: Spatial Interactions and Population Dynamics , 1994 .

[13]  S. Fortunato,et al.  Statistical physics of social dynamics , 2007, 0710.3256.

[14]  Yichen Shen,et al.  Efficient plasmonic emission by the quantum Čerenkov effect from hot carriers in graphene , 2016, Nature Communications.

[15]  Robert J. Wootton,et al.  Ecology of Teleost Fishes , 1989, Springer Netherlands.

[16]  D. Bolnick,et al.  SCARED TO DEATH? THE EFFECTS OF INTIMIDATION AND CONSUMPTION IN PREDATOR–PREY INTERACTIONS , 2005 .

[17]  L. Zanette,et al.  Perceived Predation Risk Reduces the Number of Offspring Songbirds Produce per Year , 2011, Science.

[18]  Jian Xu,et al.  Species coexistence and chaotic behavior induced by multiple delays in a food chain system , 2014 .

[19]  Joel s. Brown,et al.  ASSESSING EFFECTS OF PREDATION RISK ON FORAGING BEHAVIOR OF MULE DEER , 2001 .

[20]  Masaki Katayama,et al.  Global asymptotic stability of a predator-prey system of Holling type , 1999 .

[21]  S. L. Lima,et al.  Behavioral decisions made under the risk of predation: a review and prospectus , 1990 .

[22]  G. Szabó,et al.  Defense mechanisms of empathetic players in the spatial ultimatum game. , 2012, Physical review letters.

[23]  Eric Deleersnijder,et al.  Front dynamics in fractional-order epidemic models. , 2011, Journal of theoretical biology.

[24]  D. Baleanu,et al.  Stability analysis of Caputo fractional-order nonlinear systems revisited , 2011, Nonlinear Dynamics.

[25]  G. Samanta,et al.  Effects of dispersal speed and strong Allee effect on stability of a two-patch predator–prey model , 2018 .

[26]  G. N’Guérékata,et al.  Global stability of a Leslie-Gower-type fractional order tritrophic food chain model , 2019, Fractional Differential Calculus.

[27]  A. Lahiri,et al.  Analysis of a fractional order eco‐epidemiological model with prey infection and type 2 functional response , 2017, 1906.01226.

[28]  Xingfu Zou,et al.  Modelling the fear effect in predator–prey interactions , 2016, Journal of mathematical biology.

[29]  Robert J. Fletcher,et al.  Increased perception of predation risk to adults and offspring alters avian reproductive strategy and performance , 2014 .

[30]  Lawrence M. Dill,et al.  Living on the edge: dugongs prefer to forage in microhabitats that allow escape from rather than avoidance of predators , 2007, Animal Behaviour.

[31]  H. N. Agiza,et al.  Dynamical behavior of fractional-order Hastings-Powell food chain model and its discretization , 2015, Commun. Nonlinear Sci. Numer. Simul..

[32]  S. Das Functional Fractional Calculus , 2011 .

[33]  Ali Saleh Alshomrani,et al.  Effect of Multiple Delays in an Eco-Epidemiological Model with Strong Allee Effect , 2017, Int. J. Bifurc. Chaos.

[34]  A. Hastings,et al.  Chaos in a Three-Species Food Chain , 1991 .

[35]  D. Matignon Stability results for fractional differential equations with applications to control processing , 1996 .

[36]  Nikhil Pal,et al.  Stability and Bifurcation Analysis of a Three-Species Food Chain Model with Fear , 2015, Int. J. Bifurc. Chaos.

[37]  Justin P Suraci,et al.  Fear of large carnivores causes a trophic cascade , 2016, Nature Communications.

[38]  Jiabo Xu,et al.  Dynamic behaviors of a fractional order two-species cooperative systems with harvesting , 2016 .

[39]  Hui Chang,et al.  Dynamics Analysis and Chaotic Control of a Fractional-Order Three-Species Food-Chain System , 2020 .

[40]  T. Kaczorek Stability of fractional positive nonlinear systems , 2015 .

[41]  Manuel A. Duarte-Mermoud,et al.  Lyapunov functions for fractional order systems , 2014, Commun. Nonlinear Sci. Numer. Simul..

[42]  Sunita Gakkhar,et al.  On a Food Web Consisting of a Specialist and a Generalist Predator , 2003 .

[43]  A Sih,et al.  Optimal behavior: can foragers balance two conflicting demands? , 1980, Science.