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!----------------------------------------------------------------------
!----------------------------------------------------------------------
! fhn : Homoclinic bifurcations in Fitz-Hugh Nagumo System
!----------------------------------------------------------------------
!----------------------------------------------------------------------
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,*)
F(1)= U(2)
F(2)= PAR(1)*U(2)+U(1)*(U(1)-PAR(2))*(U(1)-1)+U(3)
F(3)= PAR(3)*U(1)/PAR(1)
IF(IJAC.EQ.0)RETURN
DFDU(1,1)= 0
DFDU(1,2)= 1
DFDU(1,3)= 0
DFDU(2,1)= 3*U(1)*U(1)-2*(1+PAR(2))*U(1)+PAR(2)
DFDU(2,2)= PAR(1)
DFDU(2,3)= 1
DFDU(3,1)= PAR(3)/PAR(1)
DFDU(3,2)= 0
DFDU(3,3)= 0
IF(IJAC.EQ.1)RETURN
DFDP(1,1)= 0
DFDP(1,2)= 0
DFDP(1,3)= 0
DFDP(2,1)= U(2)
DFDP(2,2)= -U(1)*(U(1)-1)
DFDP(2,3)= 0
DFDP(3,1)= -PAR(3)*U(1)/PAR(1)**2
DFDP(3,2)= 0
DFDP(3,3)= U(1)/PAR(1)
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
!
! COMMON block needed if IPS=9 (homoclinic bifurcations) :
INTEGER ITWIST,ISTART,IEQUIB,NFIXED,NPSI,NUNSTAB,NSTAB,NREV
COMMON /BLHOM/ ITWIST,ISTART,IEQUIB,NFIXED,NPSI,NUNSTAB,NSTAB,NREV
!----------------------------------------------------------------------
! Problem parameters (only PAR(1-9) are available to the user) :
PAR(1) = 0.21 ! c
PAR(2) = 0.2 ! a
PAR(3) = 0.0025 ! b = epsilon
PAR(11)= 0.1 ! truncated time interval
!----------------------------------------------------------------------
! If IEQUIB=1 then put the equilibrium in PAR(11+i), i=1,...,NDIM :
IF (IEQUIB.NE.0) THEN
PAR(12) = 0.0
PAR(13) = 0.0
PAR(14) = 0.0
ENDIF
!----------------------------------------------------------------------
! Distance along the unstable manifold :
IF (ISTART.EQ.3) THEN
PAR(12+NDIM*IEQUIB)=0.00001
ENDIF
!----------------------------------------------------------------------
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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