;;;;
;;;; "A Qualitative Dynamical Modelling Approach
;;;; to Capital Accumualtion in Atomistic Open-Access Fisheries"
;;;;
;;;; for Journal of Economic Dynamics and Control
;;;;
;;;; Bioe-economic main model (sections 4ff)
;;;;
;;;; Eisenack et al., V. 6.7.2004
;;;;
;;;; Start simulation with 
;;;;   ./cq -I mainmodel.run
;;;;
;;;; Result: state transition graph with 122 states
;;;; (after all standard filtering procedures).
;;;; View with: stg <CR> x <CR> k <CR> h <CR><CR>
;;;; 
;;;; STG projection contains 52 states, of which
;;;; 18 state are not final states or equilibriums.
;;;; View with: p <CR> x <CR> k <CR> h <CR><CR>

;;; Begin definition of model
  
(quantity-spaces                     
 (x (0 xmsy Q xmax) "Stock")
 (k (0 kmax)        "Capital")
 (I (0 Imax)        "Investment")
 (R (0 Rmsy Rmax)   "Recruitment")
 (h (0 MSY hmax)    "Harvest")
 (mvk (0 inf)       "-vk") ; always non-negative, only qdir matters
 (dx (minf 0 inf)   "dx")  ; dx \in (-\infty, 0) or \in (0, \infty) or =0
 (dk (minf 0 inf)   "dk")  ; dk \in (-\infty, 0) or \in (0, \infty) or =0
 (dI (minf 0 inf)   "dI")) ; dI \in (-\infty, 0) or \in (0, \infty) or =0

(constraints

 ;; Derivatives
 ((d//dt x dx))
 ((d//dt k dk))
 ((d//dt I dI))

 ((add dk k I) (0 0 0))
 ((add dx h R) (0 0 0) (0 MSY Rmsy))
 ((add dI mvk I) (0 0 0))
 
 ;; Auxiliary variables
 ((U- x R) (xmsy Rmsy) (0 0) (Q 0))
 ((mult k x h) (0 0 0))
 (((M + - -) h x k mvk))
 
 ;; Exclusion of marginal cases 
 ((cornot x h) (xmsy MSY))
 ((cornot x dx) (xmsy 0))
 ((cornot x dk) (xmsy 0))
 ((cornot x dI) (xmsy 0))
 ((cornot h dx) (MSY 0))
 ((cornot h dk) (MSY 0))
 ((cornot h dI) (MSY 0))
 ((cornot dx dk) (0 0))
 ((cornot dx dI) (0 0))
 ((cornot dk dI) (0 0))

)

;;; technical directives

(unreachable-values
  (x xmax) (k kmax) (I Imax) (R Rmax) (h hmax))

(weak-cycles)

(with-envisionment)

(no-chatter x k h)

;;; initial state of simulation

(make-initial-state 
 (x (Q dec))
 (k ((0 kmax) inc))
 (I ((0 Imax) dec))
 (h ((0 MSY) inc)))