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!----------------------------------------------------------------------
!----------------------------------------------------------------------
! nag : Heteroclinic orbits : A saddle-saddle connection
!----------------------------------------------------------------------
!----------------------------------------------------------------------
! Parameter assignment:
!
! PAR(1) , PAR(2) : a , c (parameters)
! PAR(3) , PAR(4) : eps-0 , eps-1 (radii)
! PAR(5) , PAR(6) : mu-0 , mu-1 (eigenvalues)
! PAR(7) , PAR(8) : v-0(1) , v-0(2) (eigenvector)
! PAR(9) , PAR(10): v-1(1) , v-1(2) (eigenvector)
! PAR(11) : period
!-----------------------------------------------------------------------
!-----------------------------------------------------------------------
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)
CALL FFFF(2,U,ICP,PAR,0,F,DUMMY)
PERIOD=PAR(11)
F(1)=PERIOD*F(1)
F(2)=PERIOD*F(2)
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 A,C
A=PAR(1)
C=PAR(2)
F(1)= U(2)
F(2)= C*U(2) - U(1) * (1-U(1)) * (U(1)-A)
IF(IJAC.EQ.0)RETURN
DFDU(1,1)= 0
DFDU(1,2)= 1
DFDU(2,1)= - (1-U(1))*(U(1)-A) + U(1)*(U(1)-A) - U(1)*(1-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, SIGN, R, V1, V2, X, E, U0, V0, EPS
! The following initialization is done only in the first call
IF(T==0)THEN
! Select period and connection (read from the constants-file)
PERIOD=100.
SIGN=1.0
R = 0.5*SQRT(2.D0)
V1= 1./SQRT(1+R**2)
V2= R /SQRT(1+R**2)
X = -0.5*PERIOD
E = EXP(X/SQRT(2.D0))
U0 = E/(1+E)
V0 = ( E/(1+E)**2 ) / SQRT(2.D0)
EPS= SQRT( U0**2 + V0**2 )
PAR(1)= 0.5
PAR(2)= 0
PAR(3)= EPS
PAR(4)= EPS
PAR(5)= R
PAR(6)=-R
PAR(7)= SIGN*V1
PAR(8)= SIGN*V2
PAR(9)= -SIGN*V1
PAR(10)= SIGN*V2
PAR(11)= PERIOD
PAR(12)= SIGN
ENDIF
! Specify exact solution as starting point :
PERIOD=PAR(11)
SIGN =PAR(12)
X=PERIOD*SIGN*(T-0.5)
E=DEXP(X/DSQRT(2.D0))
U(1)=E/(1+E)
U(2)=SIGN*E/(1+E)**2/DSQRT(2.D0)
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 V0(NDM),V1(NDM),G0(NDM),G1(NDM)
DOUBLE PRECISION DGDU0(NDM,NDM),DGDU1(NDM,NDM)
V0(1)=U0(1) - PAR(3)*PAR(7)
V0(2)=U0(2) - PAR(3)*PAR(8)
V1(1)=U1(1) - PAR(4)*PAR(9)
V1(2)=U1(2) - PAR(4)*PAR(10)
CALL FFFF(NDM,V0,ICP,PAR,1,G0,DGDU0)
CALL FFFF(NDM,V1,ICP,PAR,1,G1,DGDU1)
FB(1)= DGDU0(1,1)*PAR(7) + DGDU0(1,2)*PAR(8) - PAR(5)*PAR(7)
FB(2)= DGDU0(2,1)*PAR(7) + DGDU0(2,2)*PAR(8) - PAR(5)*PAR(8)
FB(3)= DGDU1(1,1)*PAR(9) + DGDU1(1,2)*PAR(10)- PAR(6)*PAR(9)
FB(4)= DGDU1(2,1)*PAR(9) + DGDU1(2,2)*PAR(10)- PAR(6)*PAR(10)
FB(5)= PAR(7)**2 + PAR(8)**2 -1
FB(6)= PAR(9)**2 + PAR(10)**2 -1
FB(7)= G0(1)
FB(8)= G0(2)
FB(9)= G1(1)
FB(10)=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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