Existence of Positive Periodic Solutions for a Neutral Delay Predator–Prey Model with Hassell–Varley Type Functional Response and Impulse

Hassell, M., Varley, G.: New inductive population model for insect parasites and its bearing on biological control. Nature 223, 1133–1136 (1969)

Wang, K.: Periodic solutions to a delayed predator-prey model with Hassell–Varley type functional response. Nonlinear Anal. Real World Appl. 12, 137–145 (2011)

Kuang, Y.: On neutral delay logistic Gauss-type predator-prey systems. Dyn. Stab. Syst. 6, 173–189 (1991)

Kuang, Y.: Delay Differential Equations with Applications in Population Dynamics. Academic Press, Boston (1993)

Zhang, F., Zheng, C.: Positive periodic solutions for the neutral ratio-dependent predator–prey model. Comput. Math. Appl. 61, 2221–2226 (2011)

Samoikleno, A.M., Perestyuk, N.A.: Impulsive Differential Equations. World Scientific, Singapore (1995)

Zavalishchhin, S.T., Sesekin, A.N.: Dynamic Impulse Systems, Theory and Applications. Kluwer Academic Publishers Group, Dordrecht (1997)

Huo, H.: Existence of positive periodic solutions of a neutral delay Lotka–Volterra system with impulses. Comput. Math. Appl. 48, 1833–1846 (2004)

Dai, B., Su, H., Hu, D.: Periodic Solution of a delayed ratio-dependent predator–prey model with monotonic functional response and impulse. Nonlinear Anal. 70, 126–134 (2009)

Wang, Q., Dai, B.: Existence of positive periodic solutions for a neutral population model with delays and impulse. Nonlinear Anal. 69, 3919–3930 (2008)

Du, Z., Feng, Z.: Periodic solutions of a neutral impulsive predator–prey model with Beddington–DeAngelis functional response with delays. J. Comput. Appl. Math. 258, 87–98 (2014)

Lv, Y., Du, Z.: Existence and global attractivity of a positive periodic solution to a Lotka–Volterra model with mutual interference and Holling III type functional response. Nonlinear Anal. Real World Appl. 12, 3654–3664 (2011)

Du, Z., Lv, Y.: Permanence and almost periodic solution of a Lotka–Volterra model with mutual interference and time delays. Appl. Math. Model. 37(3), 1054–1068 (2013)

Terry, A.J.: Predator–prey models with component Allee effect for predator reproduction. J. Math. Biol. 71, 1325–1352 (2015)

Ducrot, A., Langlais, M.: A singular reaction–diffusion system modelling prey–predator interactions: invasion and co-extinction waves. J. Differ. Equ. 253, 502–532 (2012)

Fan, M., Kuang, Y.: Dynamics of a nonautonomous predator–prey system with the Beddington–DeAngelis functional response. J. Math. Anal. Appl. 295, 15–39 (2004)

Gaines, R.E., Mawhin, J.L.: Coincidence Degree and Nonlinear Differential Equations. Springer, Berlin (1977)

Lu, S.: On the existence of positive periodic solutions to a Lotka–Volterra cooperative population model with multiple delays. Nonlinear Anal. 68, 1746–1753 (2008)

Lu, S.: On the existence of positive periodic solutions for neutral functional differential equation with multiple deviating arguments. J. Math. Anal. Appl. 280, 321–333 (2003)