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!----------------------------------------------------------------------
!----------------------------------------------------------------------
! mtn : Homoclinic bifurcations in M. Scheffer's preditor-prey model
!----------------------------------------------------------------------
!----------------------------------------------------------------------
SUBROUTINE FUNC(NDIM,U,ICP,PAR,IJAC,F,DFDU,DFDP)
! ---------- ----
IMPLICIT NONE
INTEGER, INTENT(IN) :: NDIM, ICP(*), IJAC
DOUBLE PRECISION, INTENT(IN) :: U(NDIM), PAR(*)
DOUBLE PRECISION, INTENT(OUT) :: F(NDIM)
DOUBLE PRECISION, INTENT(INOUT) :: DFDU(NDIM,NDIM), DFDP(NDIM,*)
DOUBLE PRECISION DEM,PSIZ,PSIF,PSIZU1,PSIFU2
DEM=U(2)**2+PAR(4)**2
PSIZ=0.4D0*U(1)/(0.6D0+U(1))
PSIF=PAR(2)*U(2)**2/DEM
PSIZU1=0.4D0*((1/(0.6D0+U(1)))- (U(1)/((0.6D0+U(1))**2)))
PSIFU2=2*PAR(2)*( (U(2)/DEM) -(U(2)**3/(DEM**2) ))
F(1)=0.5D0*U(1)*(1.0D0-U(1)/PAR(1))-U(2)*PSIZ+PAR(3)*PAR(1)
F(2)=0.6D0*PSIZ*U(2)-0.15D0*U(2)-PSIF
IF(IJAC.EQ.0)RETURN
DFDU(1,1)=0.5D0-U(1)/PAR(1) -U(2)*PSIZU1
DFDU(1,2)=-PSIZ
DFDU(2,1)=0.6D0*PSIZU1*U(2)
DFDU(2,2)=0.6D0*PSIZ-0.15D0-PSIFU2
IF(IJAC.EQ.1)RETURN
DFDP(1,1)=0.5D0*(U(1)/PAR(1))**2+PAR(3)
DFDP(2,1)=0.d0
DFDP(1,2)=0.0d0
DFDP(2,2)=-U(2)**2/DEM
DFDP(1,3)=PAR(1)
DFDP(2,3)=0.d0
DFDP(1,4)=0.0d0
DFDP(2,4)=2*PAR(4)*PAR(2)*U(2)**2/DEM**2
END SUBROUTINE FUNC
SUBROUTINE STPNT(NDIM,U,PAR,T)
! ----------------
! Sets parameter values for homoclinic bifurcation analysis (IPS=9).
IMPLICIT NONE
INTEGER, INTENT(IN) :: NDIM
DOUBLE PRECISION, INTENT(INOUT) :: U(NDIM),PAR(*)
DOUBLE PRECISION, INTENT(IN) :: T
!----------------------------------------------------------------------
! Problem parameters (only PAR(1-9) are available to the user) :
! PAR(11) is the trunction interval or `PERIOD'
PAR(1) = 6.0D0 ! K
PAR(2) = 0.06729762D0 ! GF
PAR(3) = 0.01D0 ! D
PAR(4) = 0.5D0 ! HZ
PAR(11)= 1046.178D0 ! truncated time interval
!----------------------------------------------------------------------
! Since IEQUIB>0 put the equilibrium in PAR(11+i), i=1,...,NDIM :
PAR(12) = 5.738626D0
PAR(13) = 0.5108401D0
!----------------------------------------------------------------------
END SUBROUTINE STPNT
SUBROUTINE PVLS
END SUBROUTINE PVLS
SUBROUTINE BCND
END SUBROUTINE BCND
SUBROUTINE ICND
END SUBROUTINE ICND
SUBROUTINE FOPT
END SUBROUTINE FOPT
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