**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30840

##### Positive Periodic Solutions in a Discrete Competitive System with the Effect of Toxic Substances

**Authors:**
Qianhong Zhang,
Changjin Xu

**Abstract:**

In this paper, a delayed competitive system with the effect of toxic substances is investigated. With the aid of differential equations with piecewise constant arguments, a discrete analogue of continuous non-autonomous delayed competitive system with the effect of toxic substances is proposed. By using Gaines and Mawhin,s continuation theorem of coincidence degree theory, a easily verifiable sufficient condition for the existence of positive solutions of difference equations is obtained.

**Keywords:**
periodic solution,
competitive system,
topological degree,
discrete time delay

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1335418

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