Monitoring in a Discrete-Time Nonlinear Age-Structured Population Model with Changing Environment

This paper is a contribution to the modeling–methodological development of application mathematical systems theory in population biology. A discrete-time nonlinear Leslie-type model considered, where both reproduction and survival rates decrease as total size increases. In this context, monitoring problem means that, from observation certain age classes function time, we want recover (estimate) whole state process (i.e., time-dependent rest classes). First, for linearization approach, conditions existence asymptotic stability positive equilibrium are obtained, then observer design method applied estimate an unknown trajectory near equilibrium, could observe single class. It also shown how can be used detect change environment that affects dynamics. The environmental supposed generated by additional dynamics (exosystem). Now, extended with exosystem, system. way, estimation obtained different (constant or periodic) changes well.