| Abstract: |
| The delay logistic equation, originating from Hutchinson, has
played a crucial role in the theory of nonlinear delay differential
equations, inspiring the development of a variety of techniques.
However, the equation has received criticisms from biological modellers
due to the lack of a mechanistic derivation.
In the talk we present a new delay logistic equation with clear biological
underpinning from cell population dynamics. We give a global analysis of
the equation showing global convergence to the positive equilibrium.
However, there exist very long transients with oscillatory patterns of
various shapes. We also show that if we add an instantaneous positive
feedback term to the classical delay logistic equation, then local stability
does not imply global stability so a Wright-type conjecture is not valid
any more. |
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