Model
Equations for Modeling
\[{{d}\over{d\,t}}\,N_{1} =\left[ b_{1} N_{1}\,\left( S_{2}\,c_{12}+S_{1}\,c_{11}\right)- d_{1} N_{1}\, \right] \label{eq:N1}\]
\[{{d}\over{d\,t}}\, N_{2} =\left[ b_{2} N_{2}\,\left( S_{2}\,c_{22}+S_{1}\,c_{21}\right)- d_{2} N_{2}\, \right] \label{eq:N2}\]
\[{{d}\over{d\,t}}\, S_{1} =\left[ a_{1} S_{1}\,\,\left( 1-{{S_{1}}\over{k_{1}}}\right)-S_{1}\,\left(N_{2}\,c_{21}+N_{1}\,c_{ 11}\right) \right] \label{eq:s1}\]
\[{{d}\over{d\,t}}\, S_{2} =\left[ a_{2} S_{2}\,\,\left( 1-{{S_{2}}\over{k_{2}}}\right)-S_{2}\,\left(N_{2}\,c_{22}+N_{1}\,c_{ 12}\right) \right] \label{eq:s2}\]
\(N_i\) : Population size of Predator \(i\).
\(i=1: Sex\)
\(i=2: Asex\)
\(S_j\) : Population size of Prey \(j\)
Original Parameters
double c11= 0.25; // consumption matrix parameter
double c12= 0.25; // consumption matrix parameter
double c21= 0.0; // consumption matrix parameter
double c22= 0.5; // consumption matrix parameter
double k1_g= 1; // carrying capacity of prey 1: good year
double k2_g= 1; // carrying capacity of prey 2: good year
No Spatial Structure
\(C=\pmatrix{c_{11}&c_{12}\cr c_{21}&c_{22}\cr }\) have entries all equal to some number, i.e. \(\alpha_{12}=\alpha_{21}=1\) in competition equations.
double c11= 0.25; // consumption matrix parameter
double c12= 0.25; // consumption matrix parameter
double c21= 0.25; // consumption matrix parameter
double c22= 0.25; // consumption matrix parameter
double k1_g= 1; // carrying capacity of prey 1: good year
double k2_g= 1; // carrying capacity of prey 2: good year
With Fluctuation
Set \(rate=0.5\)
\(rate=0\): No fluctuation
\(rate=1\): Good, Harsh year alternate
Original Parameters
double k1_g= 1; // carrying capacity of prey 1: good year
double k2_g= 1; // carrying capacity of prey 2: good year
double k1_h= 0.3; // carrying capacity of prey 1: harsh year
double k2_h= 0.3; // carrying capacity of prey 2: harsh year
No Spatial Structure
