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! ----------------------------------------------------------------------
! ----------------------------------------------------------------------
! Slow manifolds computation in the self-coupled FitzHugh-Nagumo system
! ----------------------------------------------------------------------
! Continuation of canard orbits in parameter space
! ----------------------------------------------------------------------
! Ref.: Desroches, Krauskopf and Osinga, preprint of the UoB, 2009
! URL : http://rose.bris.ac.uk/dspace/handle/1983/1312
! ----------------------------------------------------------------------
! ----------------------------------------------------------------------
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 v, h, s, epsilon, gamma, delta, T
! Define the state variables
v = U(1)
h = U(2)
s = U(3)
! Define the system parameters
epsilon = PAR(1)
gamma = PAR(2)
delta = PAR(3)
! Define the integration time as a parameter
T = PAR(11)
! Define the right-hand sides
F(1) = T * (h - (v**3 - v + 1) / 2 - gamma * s * v)
F(2) = T * (-epsilon * (2 * h + 2.6d0 * v))
F(3) = T * (-epsilon * delta * s)
END SUBROUTINE FUNC
! ----------------------------------------------------------------------
! ----------------------------------------------------------------------
SUBROUTINE STPNT
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,*)
! Define the critical manifold S as {(v,h,s) ; 2*h-v^3+v-1-s*v=0}
! (we use the fact that gamma is fixed at the value 0.5)
! Define boundary conditions */
FB(1) = U0(1) - PAR(4) ! Initial point is on the intersection between S
FB(2) = U0(2) - PAR(7) ! and the plane {h=-6.0}
FB(3) = 2*U0(2)-U0(1)**3+U0(1)-1-U0(3)*U0(1)
FB(4) = U1(1)
FB(5) = U1(2) - 0.5
FB(6) = U1(3) - PAR(6) ! End point is in a cross-section containing the
! folded node: Sigma_fn={s=0.27970}
END SUBROUTINE BCND
! ----------------------------------------------------------------------
! ----------------------------------------------------------------------
SUBROUTINE PVLS
END SUBROUTINE PVLS
! ----------------------------------------------------------------------
! ----------------------------------------------------------------------
SUBROUTINE ICND
END SUBROUTINE ICND
! ----------------------------------------------------------------------
! ----------------------------------------------------------------------
SUBROUTINE FOPT
END SUBROUTINE FOPT
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