The principle of linearized stability for size-structured population dynamics models is proved giving validity to previous stability results reported in, for example, El-Doma (2008-1). In particular, we show that if all the roots of the characteristic equation lie to the left of the imaginary axis then the steady state is locally exponentially stable, and on the other hand, if there is at least one root that lies to the right of the imaginary axis then the steady state is unstable. We also point out cases when there is resonance
The Principle of Linearized Stability for Size-Structured Population Models,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 6,
2, Article 15.
Available at: https://digitalcommons.pvamu.edu/aam/vol6/iss2/15