Food-Limited Population Models

Ravi P. Agarwal, Donal O’Regan and Samir H. Saker
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Ravi P. Agarwal: Texas A&M University-Kingsville, Department of Mathematics
Donal O’Regan: National University of Ireland, School of Mathematics, Statistics and Applied Mathematics
Samir H. Saker: Mansoura University, Department of Mathematics

Chapter Chapter 5 in Oscillation and Stability of Delay Models in Biology, 2014, pp 215-291 from Springer

Abstract: Abstract Smith [66] reasoned that a food-limited population in its growing stage requires food for both maintenance and growth, whereas, when the population has reached saturation level, food is needed for maintenance only. On the basis of these assumptions, Smith derived a model of the form 5.1 d N ( t ) d t = r N ( t ) K − N ( t ) K + c r N ( t ) $$\displaystyle{ \frac{dN(t)} {dt} = rN(t) \frac{K - N(t)} {K + crN(t)} }$$ which is called the “food limited” population Food-limitted population model . Here N, r, and K are the mass of the population, the rate of increase with unlimited food, and the value of N at saturation, respectively. The constant 1∕c is the rate of replacement of mass in the population at saturation. Since a realistic model must include some of the past history of the population, Gopalsamy, Kulenovic and Ladas introduced the delay in (5.1) and considered the equation d N ( t ) d t = r N ( t ) K − N ( t − τ ) K + c r N ( t − τ ) , $$\displaystyle{ \frac{dN(t)} {dt} = rN(t) \frac{K - N(t-\tau )} {K + crN(t-\tau )}, }$$ as the delay “food-limited” population model, where r, K, c, and τ are positive constants.

Keywords: Food-limited Population Model; Reach Saturation Levels; Kulenovic; Unlimited Food; Gopalsamy (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-3-319-06557-1_5

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