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!----------------------------------------------------------------------
!----------------------------------------------------------------------
! fsh : Heteroclinic orbits : a saddle-node copnnection
!----------------------------------------------------------------------
!----------------------------------------------------------------------
! Parameter assignment:
!
! PAR(1) : (unused)
! PAR(2) : c (wave speed)
! PAR(4) : eps-1 1 (radius)
! PAR(11) : period
! PAR(12) : mu-1 (eigenvalue at 1)
! PAR(13) , PAR(14): v(1) , v(2) (eigenvector at 1)
!-----------------------------------------------------------------------
!-----------------------------------------------------------------------
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 PERIOD,DUMMY(1)
INTEGER I
CALL FFFF(2,U,ICP,PAR,IJAC,F,DUMMY)
PERIOD=PAR(11)
DO I=1,NDIM
F(I)=PERIOD*F(I)
ENDDO
END SUBROUTINE FUNC
SUBROUTINE FFFF(NDM,U,ICP,PAR,IJAC,F,DFDU)
! ---------- ----
IMPLICIT NONE
INTEGER, INTENT(IN) :: NDM, ICP(*), IJAC
DOUBLE PRECISION, INTENT(IN) :: U(NDM), PAR(*)
DOUBLE PRECISION, INTENT(OUT) :: F(NDM)
DOUBLE PRECISION, INTENT(INOUT) :: DFDU(NDM,NDM)
DOUBLE PRECISION C
C=PAR(2)
F(1)= U(2)
F(2)= C*U(2) - U(1) * (1-U(1))
IF(IJAC.EQ.0)RETURN
DFDU(1,1)= 0
DFDU(1,2)= 1
DFDU(2,1)= -1 + 2*U(1)
DFDU(2,2)= C
END SUBROUTINE FFFF
SUBROUTINE STPNT(NDIM,U,PAR,T)
! ---------- -----
IMPLICIT NONE
INTEGER, INTENT(IN) :: NDIM
DOUBLE PRECISION, INTENT(INOUT) :: U(NDIM),PAR(*)
DOUBLE PRECISION, INTENT(IN) :: T
DOUBLE PRECISION PERIOD, C, EP1, D, RMU1, V11, V12
IF(T==0)THEN
! Set the starting period, wave speed, and radius
PERIOD=0.01
C=11.
EP1=0.001
D = SQRT(C**2+4)
PAR(2)= C
PAR(4)= EP1
PAR(11)= PERIOD
PAR(12)= (C-D)/2
PAR(13) = 1./SQRT(1+PAR(12)**2)
PAR(14)=PAR(12)/SQRT(1+PAR(12)**2)
ENDIF
C =PAR(2)
EP1 =PAR(4)
PERIOD=PAR(11)
D=SQRT(C**2+4)
RMU1= (C-D)/2
V11 = 1./SQRT(1+RMU1**2)
V12 =RMU1/SQRT(1+RMU1**2)
U(1)=1-EP1*V11
U(2)= -EP1*V12
END SUBROUTINE STPNT
SUBROUTINE BCND(NDIM,PAR,ICP,NBC,U0,U1,FB,IJAC,DBC)
! ---------- ----
IMPLICIT NONE
INTEGER, INTENT(IN) :: NDIM, ICP(*), NBC, IJAC
DOUBLE PRECISION, INTENT(IN) :: PAR(*), U0(NDIM), U1(NDIM)
DOUBLE PRECISION, INTENT(OUT) :: FB(NBC)
DOUBLE PRECISION, INTENT(INOUT) :: DBC(NBC,*)
! Local
INTEGER, PARAMETER :: NDM=2
DOUBLE PRECISION V1(NDM),G1(NDM),DGDU1(NDM,NDM)
V1(1)=U1(1) + PAR(4)*PAR(13)
V1(2)=U1(2) + PAR(4)*PAR(14)
CALL FFFF(NDM,V1,ICP,PAR,1,G1,DGDU1)
FB(1)= DGDU1(1,1)*PAR(13) + DGDU1(1,2)*PAR(14)- PAR(12)*PAR(13)
FB(2)= DGDU1(2,1)*PAR(13) + DGDU1(2,2)*PAR(14)- PAR(12)*PAR(14)
FB(3)= PAR(13)**2 + PAR(14)**2 -1
FB(4)= G1(1)
FB(5)= G1(2)
END SUBROUTINE BCND
SUBROUTINE ICND(NDIM,PAR,ICP,NINT,U,UOLD,UDOT,UPOLD,FI,IJAC,DINT)
! ---------- ----
IMPLICIT NONE
INTEGER, INTENT(IN) :: NDIM, ICP(*), NINT, IJAC
DOUBLE PRECISION, INTENT(IN) :: PAR(*)
DOUBLE PRECISION, INTENT(IN) :: U(NDIM), UOLD(NDIM), UDOT(NDIM), UPOLD(NDIM)
DOUBLE PRECISION, INTENT(OUT) :: FI(NINT)
DOUBLE PRECISION, INTENT(INOUT) :: DINT(NINT,*)
! Local
INTEGER, PARAMETER :: NDM=2
DOUBLE PRECISION F(NDM),F0(NDM),DFDU(NDM,NDM),DUMMY(1)
CALL FFFF(NDM,U ,ICP,PAR,1,F ,DFDU)
CALL FFFF(NDM,UOLD,ICP,PAR,0,F0,DUMMY)
FI(1)= ( F(1) - F0(1) ) * ( DFDU(1,1)*F(1) + DFDU(1,2)*F(2) ) &
+ ( F(2) - F0(2) ) * ( DFDU(2,1)*F(1) + DFDU(2,2)*F(2) )
END SUBROUTINE ICND
SUBROUTINE FOPT
END SUBROUTINE FOPT
SUBROUTINE PVLS
END SUBROUTINE PVLS
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