Asymptotic behaviour of a semilinear age-structured population model with a dynamics for the resource
The authors investigate a population model of the form \[ \begin{cases} u_t+u_a = -m_1(r)u,\\ v^1 = u(\ell,t)-m_2(r)v,\\ r^1 = \biggl(g(r)-H \bigl[ L(u,v)\bigr] \biggr)r,\\ {\phantom =} u(0,t)=bv(t),\;u(a,0)= u_0(a),\;v(0)=v_0,\;r(0) =r_0. \end{cases} \tag{1} \] Here, the age \(a\in(0,\ell)\), \(\ell=\) maturation age, \(m_1 (r)\), \(m_2(r)=\) death rates, \(m_1\), for juveniles, \(m_2\) for adults. The second equation in (1) describes the transition rate from juveniles to adults. The third equation describes the dynamics of the resource \(r(t)\). The authors use semigroup theory to prove existence, uniqueness and continuous dependence on initial age distributions. Stability of equilibrium solutions and bifurcation is also discussed in depth and complemented with numerical results.
scientific article; zbMATH DE number 1781898
scientific article