adding Lotka Volterra to model library

inst/starter_models/lotka_volterra/README.md

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+---
+title: "Lotka-Volterra"
+index_entry: "simple two-species competition model"
+author: Jennifer Freeman
+---
+
+- $X$ - number of individuals in species $X$  
+- $Y$ - number of individuals in species $Y$ 
+- $r_i$ - growth rate of species $I$
+- $a_{ij}$ - intra/inter-specific density dependence, ``effect of species $j$ on species $i$'' (Hastings, 1997)
+
+$$
+\begin{align*}
+\frac{dX}{dt} &= r_x X (1 - a_{xx}X - a_{xy}Y) \\
+\frac{dY}{dt} &= r_y Y (1 - a_{yy}Y - a_{yx}X)
+\end{align*}
+$$
+
+Hastings, A. (1997). Competition. In: Population Biology. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2731-9_7

inst/starter_models/lotka_volterra/model.R

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+library(macpan2)
+
+## expression lists
+###################################################
+
+## free form computations for convenience
+## none
+
+## absolute flow rates (per time only)
+## reference 
+flow_rates = list(
+  ## growth rate of species X and Y
+    growth_x ~ rx * X
+  , growth_y ~ ry * Y
+  ## intraspecific effect
+  ## species X on X
+  , intraspecific_x ~ growth_x * axx * X
+  ## species Y on Y
+  , intraspecific_y ~ growth_y * ayy * Y
+  ## interspecific effect
+  ## species X on Y
+  , interspecific_xy ~ growth_x * ayx * Y
+  ## species Y on X
+  , interspecific_yx ~ growth_y * axy * X
+)
+
+## state updates
+state_updates = list(
+    X ~ X + growth_x - intraspecific_x - interspecific_xy
+  , Y ~ Y + growth_y - intraspecific_y - interspecific_yx
+)
+
+## simple unstructured scalar expression
+expr_list =  ExprList(
+  during = c(
+      flow_rates
+    , state_updates
+  )
+)