Existence of positive periodic solutions for a periodic predator–prey model with fear effect and general functional responses

Abstract

This paper investigates the existence of positive periodic solutions for a periodic predator-prey model with fear effect and general functional responses. The general functional responses can cover the Holling types II and III functional response, the Beddington–DeAngelis functional response, the Crowley–Martin functional response, the ratio-dependent type with Michaelis–Menten type functional response, etc. Some new sufficient conditions for the existence of positive periodic solutions of the model are obtained by employing the continuation theorem of coincidence degree theory and some ingenious estimation techniques for the upper and lower bounds of the a priori solutions of the corresponding operator equation. Our results considerably improve and extend some known results.

A Unified Approach to Solvability and Stability of Multipoint BVPs for Langevin and Sturm–Liouville Equations with CH–Fractional Derivatives and Impulses via Coincidence Theory

“…Only a small number of published papers deal with the solvability and stability of implicit Hadamard fractional differential equations (see [48][49][50][51][52][53][54][55][56]). Some academic researchers have applied the theory of coincidence degree to study the solvability of integer-order nonlinear functional differential equations and have achieved fruitful results (see [57][58][59][60][61][62][63][64][65][66][67][68]). In the theory of coincidence degree, the construction of relevant operators is highly skilled, which brings difficulties to the application of this method.…”