Positive periodic solutions for an impulsive neutral delay model of single-species population growth on time scales
نویسندگان
چکیده
where a, β, b, c, τ are nonnegative continuous periodic functions. Since then, different classes of neutral functional differential equations have been extensively studied, we refer the readers to [1-5] and the references therein. However, in the natural world, there are many species whose developing processes are both continuous and discrete. Hence, using the only differential equation or difference equation can’t accurately describe the law of their developments. Therefore, there is a need to establish correspondent dynamic models on new time scales. The theory of calculus on time scales (see [6] and references cited therein) was initiated by Stefan Hilger [7] in order to unify continuous and discrete analysis, and it has a tremendous potential for applications and has recently received much attention since his foundational work (see, e.g., 8-14). Therefore, it is practicable to study that on time scales which can unify the continuous and discrete situations. Motivated by above, the aim of this paper is to establish sufficient conditions for the existence of positive periodic solutions for a neutral delay model of single-species population growth on time scales. However, it is known that many real world phenomena often behave in a piecewise continuous frame interlaced with abrupt changes. Thus, the choice of system accompanied with impulsive conditions is much more appropriate. Consider the following impulsive neutral delay model of single-species population growth on time scales x∆(t) = x(t) [ r(t)− a(t)x(t)
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