Bifurcation analysis of a diffusive predator–prey system with nonmonotonic functional response
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Chen, S., Jianshe, Y.: Dynamics of a diffusive predator–prey system with a nonlinear growth rate for the predator. J. Differ. Equ. 260(11), 7923–7939 (2016)
Du, Y., Shi, J.: A diffusive predator-prey model with a protection zone. J. Differ. Equ. 229(1), 63–91 (2006)
Faria, T.: Stability and bifurcation for a delayed predator–prey model and the effect of diffusion. J. Math. Anal. Appl. 254(2), 433–463 (2001)
Guo, S.: Patterns in a nonlocal time-delayed reaction–diffusion equation. Zeitschrift für angewandte Mathematik und Physik 69(10), 1–31 (2018)
Guo, S.: Generalized Hopf bifurcation for neutral functional differential equations. Int. J. Bifurc. Chaos 26(14), 1650231 (2016)
Guo, S.: Stability and bifurcation in a reaction–diffusion model with nonlocal delay effect. J. Differ. Equ. 259(4), 1409–1448 (2015)
Guo, S., Man, J.: Patterns in hierarchical networks of neuronal oscillators with $$\mathbb{D}_3\times \mathbb{Z}_3$$ D 3 × Z 3 symmetry. J. Differ. Equ. 254(8), 3501–3529 (2013)
Guo, S., Wu, J.: Bifurcation Theory of Functional Differential Equations, vol. 184. Springer, New York (2013)
Guo, S., Yan, S.: Hopf bifurcation in a diffusive Lotka–Volterra type system with nonlocal delay effect. J. Differ. Equ. 260(1), 781–817 (2016)
Guo, S., Yuan, Y.: Pattern formation in a ring network with delay. Math. Models Methods Appl. Sci. 19(10), 1797–1852 (2009)
Henry, D.: Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Mathematics. Springer, Berlin (1993)
Holling, C.S.: Some characteristics of simple types of predation and parasitism. Can. Entomol. 91(1), 385–398 (1959)
Kazarinoff, N.D., Van Den Driessche, P.: A model predator–prey system with functional response. Math. Biosci. 39(1), 125–134 (1978)
Kuto, K., Tsujikawa, T.: Limiting structure of steady-states to the lotka–Lvolterra competition model with large diffusion and advection. J. Differ. Equ. 258(5), 1801–1858 (2015)
Kuznetsov, Y.A.: Elements of Applied Bifurcation Theory. Applied Mathematical Sciences, vol. 112, 2nd edn. Springer, Berlin (1998)
Lotka, A.J.: Elements of Physical Biology. Williams & Wilkins Company, Philadelphia (1925)
Ma, L., Guo, S.: Stability and bifurcation in a diffusive Lotka–Volterra system with delay. Comput. Math. Appl. 72(1), 147–177 (2016)
Medvinsky, A.B., Petrovskii, S.V., Tikhonova, I.A., Malchow, H., Li, B.-L.: Spatiotemporal complexity of plankton and fish dynamics. SIAM Rev. 44(3), 311–370 (2002)
Murray, J.D.: Mathematical Biology: I. An Introduction. Interdisciplinary Applied Mathematics. Springer, New York (2011)
Owen, M.R., Lewis, M.A.: How predation can slow, stop or reverse a prey invasion. Bull. Math. Biol. 63(4), 655 (2001)
Peng, R., Shi, J.: Non-existence of non-constant positive steady states of two holling type-II predator–prey systems: strong interaction case. J. Differ. Equ. 247(3), 866–886 (2009)
Rabinowitz, P.H.: Some global results for nonlinear eigenvalue problems. J. Funct. Anal. 7(3), 487–513 (1971)
Seo, G., Kot, M.: A comparison of two predator–prey models with Hollings type I functional response. Math. Biosci. 212(2), 161–179 (2008)
Sokol, W., Howell, J.A.: Kinetics of phenol oxidation by washed cells. Biotechnol. Bioeng. 23(9), 2039–2049 (1981)
Wang, J.F., Wang, Y.W.: Bifurcation analysis in a diffusive Segel–Jackson model. J. Math. Anal. Appl. 415(1), 204–216 (2014)
Wang, J.: Spatiotemporal patterns of a homogeneous diffusive predator–prey system with holling type III functional response. J. Dyn. Differ. Equ. 29(4), 1383–1409 (2017)
Wang, J., Wei, J., Shi, J.: Global bifurcation analysis and pattern formation in homogeneous diffusive predator–prey systems. J. Differ. Equ. 260(4), 3495–3523 (2016)
Wu, J.: Theory and Applications of Partial Functional Differential Equations, vol. 119. Springer, Berlin (1996)
Xiao, D., Ruan, S.: Global analysis in a predator–prey system with nonmonotonic functional response. SIAM J. Appl. Math. 61(4), 1445–1472 (2001)
Xiao, D., Zhu, H.: Multiple focus and hopf bifurcations in a predator–prey system with nonmonotonic functional response. SIAM J. Appl. Math. 66(3), 802–819 (2006)
Yan, S., Guo, S.: Bifurcation phenomena in a Lotka–Volterra model with cross-diffusion and delay effect. Int. J. Bifurc. Chaos 27(7), 1750105 (2017)
Yan, S., Guo, S.: Stability analysis of a stage structure model with spatiotemporal delay effect. Comput. Math. Appl. 73(2), 310–326 (2017)
Yan, X., Li, W.: Stability of bifurcating periodic solutions in a delayed reaction–diffusion population model. Nonlinearity 23(6), 1414–1431 (2010)
Yi, F., Wei, J., Shi, J.: Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator–prey system. J. Differ. Equ. 246(5), 1944–1977 (2009)
Zhang, L., Guo, S.: Hopf bifurcation in delayed van der Pol oscillators. Nonlinear Dyn. 71(3), 555–568 (2013)
Zou, R., Guo, S.: Dynamics in a diffusive predator–prey system with ratio-dependent predator influence. Comput. Math. Appl. 75, 1237–1258 (2018)