Multiple periodic solutions of an impulsive predator–prey model with Holling-type IV functional response

• Published in: Mathematical and computer modelling Vol. 49; no. 9; pp. 1829 - 1836
• Main Authors: Wang, Qi, Dai, Binxiang, Chen, Yuming
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.05.2009; Elsevier
• Subjects: Coincidence degree; Exact sciences and technology; Holling-type IV functional response; Impulse; Mathematical analysis; Mathematics; Methods of scientific computing (including symbolic computation, algebraic computation); Numerical analysis. Scientific computation; Operator theory; Periodic solution; Predator–prey model; Real functions; Sciences and techniques of general use; Holling-type IV functional response; Periodic solution; Predator–prey model; Impulse; Coincidence degree; Existence condition; Existence of solution; Periodic function; Continuous function; Sufficient condition; Scientific computation; Applied mathematics; Mathematical model; Predator-prey model; Computer aided analysis
• ISSN: 0895-7177; 1872-9479
• DOI: 10.1016/j.mcm.2008.09.008

An impulsive periodic predator–prey model with Holling-type IV functional response is considered. Using the continuation theorem of coincidence degree theory, we present an easily verifiable sufficient condition on the existence of multiple periodic solutions. It is important to point out that we establish a better estimation on the difference between the supremum and infimum of a differentiable piecewise continuous periodic function. As illustrated in this paper, with the help of this estimation, many existing results can be improved.