Parameters: m (mortality of prey): homogeneous stressor and betas (eating/reproducing rate of predator) => spatial stressor.
Issues:
a) The time to reach 'steady' state is very long (around 2000 to 5000 time steps)
b) Equilibria: Finding coexistence equilibria (iii below) and whether other eq. are stable is hard.
Eq. are:
i) No prey, no predator
ii) finite prey, no predator
iii) coexistence of prey and predator.
Eq. (i) and (ii) will always exist. For some parameter values we will have coexistence. Due to stochastic effects, its difficult to know what is the steady state.
c) Cyclical behaviour in coexistence: Most scenarios of coexistence we have manually tried so far end up in oscillations. We may need to think how to quantify it.
d) Constructing phase diagram: will require careful initial dependence scan. Also, what kind of bifurcations are there? (Hopf vs homoclinic, vs saddle node, etc).
e) Computing indicators in cyclic systems is tricky. Do we average over multiple time step snapshots (with different densities?). How to calculate temporal indicators (with or without detrending cyclic oscillations)? How to calculate spatial indicators?
Parameters: m (mortality of prey): homogeneous stressor and betas (eating/reproducing rate of predator) => spatial stressor.
Issues: a) The time to reach 'steady' state is very long (around 2000 to 5000 time steps)
b) Equilibria: Finding coexistence equilibria (iii below) and whether other eq. are stable is hard. Eq. are: i) No prey, no predator ii) finite prey, no predator iii) coexistence of prey and predator.
Eq. (i) and (ii) will always exist. For some parameter values we will have coexistence. Due to stochastic effects, its difficult to know what is the steady state.
c) Cyclical behaviour in coexistence: Most scenarios of coexistence we have manually tried so far end up in oscillations. We may need to think how to quantify it.
d) Constructing phase diagram: will require careful initial dependence scan. Also, what kind of bifurcations are there? (Hopf vs homoclinic, vs saddle node, etc).
e) Computing indicators in cyclic systems is tricky. Do we average over multiple time step snapshots (with different densities?). How to calculate temporal indicators (with or without detrending cyclic oscillations)? How to calculate spatial indicators?