Finding equilibrium states

Hello! I try find equilibrium states for system:

function HR_mem(u, p, t)
    function sigma(x)
        return 1.0 / ( 1.0 + exp( -10.0 * ( x  - ( - 0.25 ) ) ) )
    end
    memristor(z, k1_me, k2_me) = k1_me + k2_me * z^2

    a, b, c, d, s, xr, r,  I, vs, k1, k2, k1_me, k2_me  = p
    x1, y1, z1, x2, y2, z2, z = u
    
    du1 = y1 + b * x1 ^ 2 - a * x1 ^3 - z1 + I - k1 * ( x1 - vs ) * sigma(x2) + memristor(z, k1_me, k2_me)*(x2 - x1)
    du2 = c - d * x1 ^2 - y1
    du3 = r * ( s * ( x1 - xr ) - z1 )                                                                                                                                          
    
    du4 = y2 + b * x2 ^ 2 - a * x2 ^3 - z2 + I - k2 * ( x2 - vs ) * sigma(x1) + memristor(z, k1_me, k2_me)*(x1 - x2)
    du5 = c - d * x2 ^2 - y2
    du6 = r * ( s * ( x2 - xr ) - z2 )

    du7 = x1 - x2
    
    return SVector(du1, du2, du3, du4, du5, du6, du7)
end

@inbounds function jacob_HR_mem(u, p, t)

    a, b, c, d, s, xr, r,  I, vs, k1, k2, k1_me, k2_me  = p
    x1, y1, z1, x2, y2, z2, z = u

    function sigma(x)
        return 1.0 / ( 1.0 + exp( -10.0 * ( x  - ( - 0.25 ) ) ) )
    end
    memristor(z, k1_me, k2_me) = k1_me + k2_me * z^2

    sigmax1der = 10.0 * exp( -10.0*( x1 + 0.25 ) ) / ( 1.0 + exp( -10.0*( x1 + 0.25 ) ) )^2
    sigmax2der = 10.0 * exp( -10.0*( x2 + 0.25 ) ) / ( 1.0 + exp( -10.0*( x2 + 0.25 ) ) )^2
    
    x1x1 = 2.0*b*x1 - 3.0 * a * x1^2 - k1 * sigma(x2) - memristor(z, k1_me, k2_me)
    x1y1 = 1.0
    x1z1 = -1.0
    x1x2 = -k1 * ( x1 - vs ) * sigmax2der + memristor(z, k1_me, k2_me)
    x1y2 = 0.0
    x1z2 = 0.0
    x1z = k2_me * 2.0 * z * ( x2 - x1 )

    y1x1 = -2.0 * d * x1
    y1y1 = -1.0
    y1z1 = 0.0
    y1x2 = 0.0
    y1y2 = 0.0
    y1z2 = 0.0
    y1z = 0.0

    z1x1 = r * s
    z1y1 = 0.0
    z1z1 = -r
    z1x2 = 0.0
    z1y2 = 0.0
    z1z2 = 0.0
    z1z = 0.0

    zx1 = 1.0
    zy1 = 0.0
    zz1 = 0.0
    zx2 = -1.0
    zy2 = 0.0
    zz2 = 0.0

    zz = 0.0

    # -------------------------------------

    x2x2 = 2.0*b*x2 - 3.0 * a * x2^2 - k2 * sigma(x1) - memristor(z, k1_me, k2_me)
    x2y2 = 1.0
    x2z2 = -1.0
    x2x1 = -k2 * ( x2 - vs ) * sigmax1der + memristor(z, k1_me, k2_me)
    x2y1 = 0.0
    x2z1 = 0.0
    x2z = k2_me * 2.0 * z * ( x1 - x2 )

    y2x2 = -2.0 * d * x2
    y2y2 = -1.0
    y2z2 = 0.0
    y2x1 = 0.0
    y2y1 = 0.0
    y2z1 = 0.0
    y2z = 0.0

    z2x2 = r * s
    z2y2 = 0.0
    z2z2 = -r
    z2x1 = 0.0
    z2y1 = 0.0
    z2z1 = 0.0
    z2z = 0.0

    zx2 = -1.0
    zy2 = 0.0
    zz2 = 0.0
    zx1 = 1.0
    zy1 = 0.0
    zz1 = 0.0

    SMatrix{7,7}(x1x1, y1x1, z1x1, x2x1, y2x1, z2x1, zx1,
    x1y1, y1y1, z1y1, x2y1, y2y1, z2y1, zy1,
    x1z1, y1z1, z1z1, x2z1, y2z1, z2z1, zz1,
    x1x2, y1x2, z1x2, x2x2, y2x2, z2x2, zx2,
    x1y2, y1y2, z1y2, x2y2, y2y2, z2y2, zy2,
    x1z2, y1z2, z1z2, x2z2, y2z2, z2z2, zz2,
    x1z, y1z, z1z, x2z, y2z, z2z, zz)
end

a = 1.0; b = 3.0; c = 1.0; d = 5.0;
xr = -1.6; r = 0.01; s = 5.0; I = 4.0; xv = 2.0;                                                                                                                        
k1= -0.17; k2 = -0.17;
k1_me= 0.331
k2_me = 0.0
u0 = [-1.5, 0.0, 0.0, -2.5, 0.0, 0.0, 0.0]
p = [a, b, c, d, s, xr, r, I, xv, k1, k2, k1_me, k2_me];

tt = 5000; time = 1000; tstep = 0.001
integ_set = (alg = Vern9(), adaptive = false, dt = tstep)

ds = CoupledODEs(HR_mem, u0, p, diffeq = integ_set)
fp, eigs, stable = fixedpoints(ds, box, jacob_HR_mem)

I get the following error. How to understand what it is connected with?

LinearAlgebra.SingularException(7)

Stacktrace:
  [1] macro expansion
    @ C:\Users\Alex\.julia\packages\StaticArrays\O6dgq\src\lu.jl:84 [inlined]
  [2] _lu(A::SMatrix{7, 7, IntervalArithmetic.Interval{Float64}, 49}, pivot::Val{true}, check::Bool)
    @ StaticArrays C:\Users\Alex\.julia\packages\StaticArrays\O6dgq\src\lu.jl:73
  [3] #lu#488
    @ C:\Users\Alex\.julia\packages\StaticArrays\O6dgq\src\lu.jl:50 [inlined]
  [4] lu
    @ C:\Users\Alex\.julia\packages\StaticArrays\O6dgq\src\lu.jl:49 [inlined]
  [5] #lu#495
    @ C:\Users\Alex\.julia\packages\StaticArrays\O6dgq\src\lu.jl:54 [inlined]
  [6] lu
    @ C:\Users\Alex\.julia\packages\StaticArrays\O6dgq\src\lu.jl:54 [inlined]
  [7] macro expansion
    @ C:\Users\Alex\.julia\packages\StaticArrays\O6dgq\src\inv.jl:79 [inlined]
  [8] _inv
    @ C:\Users\Alex\.julia\packages\StaticArrays\O6dgq\src\inv.jl:74 [inlined]
  [9] inv
    @ C:\Users\Alex\.julia\packages\StaticArrays\O6dgq\src\inv.jl:5 [inlined]
 [10] 𝒦(f::ChaosTools.var"#15#16"{CoupledODEs{false, 7, OrdinaryDiffEq.ODEIntegrator{Vern9{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}, false, SVector{7, Float64}, Nothing, Float64, Vector{Float64}, Float64, Float64, Float64, Float64, Vector{SVector{7, Float64}}, ODESolution{Float64, 2, Vector{SVector{7, Float64}}, Nothing, Nothing, Vector{Float64}, Vector{Vector{SVector{7, Float64}}}, ODEProblem{SVector{7, Float64}, Tuple{Float64, Float64}, false, Vector{Float64}, ODEFunction{false, SciMLBase.AutoSpecialize, typeof(HR_mem), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, Vern9{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}, OrdinaryDiffEq.InterpolationData{ODEFunction{false, SciMLBase.AutoSpecialize, typeof(HR_mem), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, Vector{SVector{7, Float64}}, Vector{Float64}, Vector{Vector{SVector{7, Float64}}}, OrdinaryDiffEq.Vern9ConstantCache}, DiffEqBase.Stats, Nothing}, ODEFunction{false, SciMLBase.AutoSpecialize, typeof(HR_mem), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, OrdinaryDiffEq.Vern9ConstantCache, OrdinaryDiffEq.DEOptions{Float64, Float64, Float64, Float64, PIController{Rational{Int64}}, typeof(DiffEqBase.ODE_DEFAULT_NORM), typeof(LinearAlgebra.opnorm), Bool, CallbackSet{Tuple{}, Tuple{}}, typeof(DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN), typeof(DiffEqBase.ODE_DEFAULT_PROG_MESSAGE), typeof(DiffEqBase.ODE_DEFAULT_UNSTABLE_CHECK), DataStructures.BinaryHeap{Float64, DataStructures.FasterForward}, DataStructures.BinaryHeap{Float64, DataStructures.FasterForward}, Nothing, Nothing, Float64, Tuple{}, Tuple{}, Tuple{}}, SVector{7, Float64}, Float64, Nothing, OrdinaryDiffEq.DefaultInit}, Vector{Float64}}, Vector{Float64}}, jacobian::ChaosTools.var"#17#18"{typeof(jacob_HR_mem), Vector{Float64}}, X::IntervalBox{7, Float64}, α::Float64)
    @ IntervalRootFinding C:\Users\Alex\.julia\packages\IntervalRootFinding\gKaGR\src\contractors.jl:52
 [11] #37
    @ C:\Users\Alex\.julia\packages\IntervalRootFinding\gKaGR\src\contractors.jl:115 [inlined]
 [12] determine_region_status(op::IntervalRootFinding.var"#37#38"{IntervalRootFinding.Krawczyk{ChaosTools.var"#15#16"{CoupledODEs{false, 7, OrdinaryDiffEq.ODEIntegrator{Vern9{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}, false, SVector{7, Float64}, Nothing, Float64, Vector{Float64}, Float64, Float64, Float64, Float64, Vector{SVector{7, Float64}}, ODESolution{Float64, 2, Vector{SVector{7, Float64}}, Nothing, Nothing, Vector{Float64}, Vector{Vector{SVector{7, Float64}}}, ODEProblem{SVector{7, Float64}, Tuple{Float64, Float64}, false, Vector{Float64}, ODEFunction{false, SciMLBase.AutoSpecialize, typeof(HR_mem), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, Vern9{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}, OrdinaryDiffEq.InterpolationData{ODEFunction{false, SciMLBase.AutoSpecialize, typeof(HR_mem), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, Vector{SVector{7, Float64}}, Vector{Float64}, Vector{Vector{SVector{7, Float64}}}, OrdinaryDiffEq.Vern9ConstantCache}, DiffEqBase.Stats, Nothing}, ODEFunction{false, SciMLBase.AutoSpecialize, typeof(HR_mem), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, OrdinaryDiffEq.Vern9ConstantCache, OrdinaryDiffEq.DEOptions{Float64, Float64, Float64, Float64, PIController{Rational{Int64}}, typeof(DiffEqBase.ODE_DEFAULT_NORM), typeof(LinearAlgebra.opnorm), Bool, CallbackSet{Tuple{}, Tuple{}}, typeof(DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN), typeof(DiffEqBase.ODE_DEFAULT_PROG_MESSAGE), typeof(DiffEqBase.ODE_DEFAULT_UNSTABLE_CHECK), DataStructures.BinaryHeap{Float64, DataStructures.FasterForward}, DataStructures.BinaryHeap{Float64, DataStructures.FasterForward}, Nothing, Nothing, Float64, Tuple{}, Tuple{}, Tuple{}}, SVector{7, Float64}, Float64, Nothing, OrdinaryDiffEq.DefaultInit}, Vector{Float64}}, Vector{Float64}}, ChaosTools.var"#17#18"{typeof(jacob_HR_mem), Vector{Float64}}}, Float64}, f::ChaosTools.var"#15#16"{CoupledODEs{false, 7, OrdinaryDiffEq.ODEIntegrator{Vern9{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}, false, SVector{7, Float64}, Nothing, Float64, Vector{Float64}, Float64, Float64, Float64, Float64, Vector{SVector{7, Float64}}, ODESolution{Float64, 2, Vector{SVector{7, Float64}}, Nothing, Nothing, Vector{Float64}, Vector{Vector{SVector{7, Float64}}}, ODEProblem{SVector{7, Float64}, Tuple{Float64, Float64}, false, Vector{Float64}, ODEFunction{false, SciMLBase.AutoSpecialize, typeof(HR_mem), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, Vern9{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}, OrdinaryDiffEq.InterpolationData{ODEFunction{false, SciMLBase.AutoSpecialize, typeof(HR_mem), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, Vector{SVector{7, Float64}}, Vector{Float64}, Vector{Vector{SVector{7, Float64}}}, OrdinaryDiffEq.Vern9ConstantCache}, DiffEqBase.Stats, Nothing}, ODEFunction{false, SciMLBase.AutoSpecialize, typeof(HR_mem), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, OrdinaryDiffEq.Vern9ConstantCache, OrdinaryDiffEq.DEOptions{Float64, Float64, Float64, Float64, PIController{Rational{Int64}}, typeof(DiffEqBase.ODE_DEFAULT_NORM), typeof(LinearAlgebra.opnorm), Bool, CallbackSet{Tuple{}, Tuple{}}, typeof(DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN), typeof(DiffEqBase.ODE_DEFAULT_PROG_MESSAGE), typeof(DiffEqBase.ODE_DEFAULT_UNSTABLE_CHECK), DataStructures.BinaryHeap{Float64, DataStructures.FasterForward}, DataStructures.BinaryHeap{Float64, DataStructures.FasterForward}, Nothing, Nothing, Float64, Tuple{}, Tuple{}, Tuple{}}, SVector{7, Float64}, Float64, Nothing, OrdinaryDiffEq.DefaultInit}, Vector{Float64}}, Vector{Float64}}, R::IntervalRootFinding.Root{IntervalBox{7, Float64}})
    @ IntervalRootFinding C:\Users\Alex\.julia\packages\IntervalRootFinding\gKaGR\src\contractors.jl:153
 [13] Krawczyk
    @ C:\Users\Alex\.julia\packages\IntervalRootFinding\gKaGR\src\contractors.jl:116 [inlined]
 [14] Krawczyk
    @ C:\Users\Alex\.julia\packages\IntervalRootFinding\gKaGR\src\contractors.jl:115 [inlined]
 [15] process(search::IntervalRootFinding.DepthFirstSearch{IntervalBox{7, Float64}, IntervalRootFinding.Krawczyk{ChaosTools.var"#15#16"{CoupledODEs{false, 7, OrdinaryDiffEq.ODEIntegrator{Vern9{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}, false, SVector{7, Float64}, Nothing, Float64, Vector{Float64}, Float64, Float64, Float64, Float64, Vector{SVector{7, Float64}}, ODESolution{Float64, 2, Vector{SVector{7, Float64}}, Nothing, Nothing, Vector{Float64}, Vector{Vector{SVector{7, Float64}}}, ODEProblem{SVector{7, Float64}, Tuple{Float64, Float64}, false, Vector{Float64}, ODEFunction{false, SciMLBase.AutoSpecialize, typeof(HR_mem), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, Vern9{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}, OrdinaryDiffEq.InterpolationData{ODEFunction{false, SciMLBase.AutoSpecialize, typeof(HR_mem), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, Vector{SVector{7, Float64}}, Vector{Float64}, Vector{Vector{SVector{7, Float64}}}, OrdinaryDiffEq.Vern9ConstantCache}, DiffEqBase.Stats, Nothing}, ODEFunction{false, SciMLBase.AutoSpecialize, typeof(HR_mem), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, OrdinaryDiffEq.Vern9ConstantCache, OrdinaryDiffEq.DEOptions{Float64, Float64, Float64, Float64, PIController{Rational{Int64}}, typeof(DiffEqBase.ODE_DEFAULT_NORM), typeof(LinearAlgebra.opnorm), Bool, CallbackSet{Tuple{}, Tuple{}}, typeof(DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN), typeof(DiffEqBase.ODE_DEFAULT_PROG_MESSAGE), typeof(DiffEqBase.ODE_DEFAULT_UNSTABLE_CHECK), DataStructures.BinaryHeap{Float64, DataStructures.FasterForward}, DataStructures.BinaryHeap{Float64, DataStructures.FasterForward}, Nothing, Nothing, Float64, Tuple{}, Tuple{}, Tuple{}}, SVector{7, Float64}, Float64, Nothing, OrdinaryDiffEq.DefaultInit}, Vector{Float64}}, Vector{Float64}}, ChaosTools.var"#17#18"{typeof(jacob_HR_mem), Vector{Float64}}}, Float64}, r::IntervalRootFinding.Root{IntervalBox{7, Float64}})
    @ IntervalRootFinding C:\Users\Alex\.julia\packages\IntervalRootFinding\gKaGR\src\roots.jl:56
 [16] iterate(search::IntervalRootFinding.DepthFirstSearch{IntervalBox{7, Float64}, IntervalRootFinding.Krawczyk{ChaosTools.var"#15#16"{CoupledODEs{false, 7, OrdinaryDiffEq.ODEIntegrator{Vern9{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}, false, SVector{7, Float64}, Nothing, Float64, Vector{Float64}, Float64, Float64, Float64, Float64, Vector{SVector{7, Float64}}, ODESolution{Float64, 2, Vector{SVector{7, Float64}}, Nothing, Nothing, Vector{Float64}, Vector{Vector{SVector{7, Float64}}}, ODEProblem{SVector{7, Float64}, Tuple{Float64, Float64}, false, Vector{Float64}, ODEFunction{false, SciMLBase.AutoSpecialize, typeof(HR_mem), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, Vern9{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}, OrdinaryDiffEq.InterpolationData{ODEFunction{false, SciMLBase.AutoSpecialize, typeof(HR_mem), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, Vector{SVector{7, Float64}}, Vector{Float64}, Vector{Vector{SVector{7, Float64}}}, OrdinaryDiffEq.Vern9ConstantCache}, DiffEqBase.Stats, Nothing}, ODEFunction{false, SciMLBase.AutoSpecialize, typeof(HR_mem), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, OrdinaryDiffEq.Vern9ConstantCache, OrdinaryDiffEq.DEOptions{Float64, Float64, Float64, Float64, PIController{Rational{Int64}}, typeof(DiffEqBase.ODE_DEFAULT_NORM), typeof(LinearAlgebra.opnorm), Bool, CallbackSet{Tuple{}, Tuple{}}, typeof(DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN), typeof(DiffEqBase.ODE_DEFAULT_PROG_MESSAGE), typeof(DiffEqBase.ODE_DEFAULT_UNSTABLE_CHECK), DataStructures.BinaryHeap{Float64, DataStructures.FasterForward}, DataStructures.BinaryHeap{Float64, DataStructures.FasterForward}, Nothing, Nothing, Float64, Tuple{}, Tuple{}, Tuple{}}, SVector{7, Float64}, Float64, Nothing, OrdinaryDiffEq.DefaultInit}, Vector{Float64}}, Vector{Float64}}, ChaosTools.var"#17#18"{typeof(jacob_HR_mem), Vector{Float64}}}, Float64}, wt::IntervalRootFinding.BBTree{IntervalRootFinding.Root{IntervalBox{7, Float64}}})
    @ IntervalRootFinding C:\Users\Alex\.julia\packages\IntervalRootFinding\gKaGR\src\branch_and_bound.jl:307
 [17] iterate
    @ C:\Users\Alex\.julia\packages\IntervalRootFinding\gKaGR\src\branch_and_bound.jl:303 [inlined]
 [18] branch_and_prune(r::IntervalRootFinding.Root{IntervalBox{7, Float64}}, contractor::IntervalRootFinding.Krawczyk{ChaosTools.var"#15#16"{CoupledODEs{false, 7, OrdinaryDiffEq.ODEIntegrator{Vern9{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}, false, SVector{7, Float64}, Nothing, Float64, Vector{Float64}, Float64, Float64, Float64, Float64, Vector{SVector{7, Float64}}, ODESolution{Float64, 2, Vector{SVector{7, Float64}}, Nothing, Nothing, Vector{Float64}, Vector{Vector{SVector{7, Float64}}}, ODEProblem{SVector{7, Float64}, Tuple{Float64, Float64}, false, Vector{Float64}, ODEFunction{false, SciMLBase.AutoSpecialize, typeof(HR_mem), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, Vern9{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}, OrdinaryDiffEq.InterpolationData{ODEFunction{false, SciMLBase.AutoSpecialize, typeof(HR_mem), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, Vector{SVector{7, Float64}}, Vector{Float64}, Vector{Vector{SVector{7, Float64}}}, OrdinaryDiffEq.Vern9ConstantCache}, DiffEqBase.Stats, Nothing}, ODEFunction{false, SciMLBase.AutoSpecialize, typeof(HR_mem), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, OrdinaryDiffEq.Vern9ConstantCache, OrdinaryDiffEq.DEOptions{Float64, Float64, Float64, Float64, PIController{Rational{Int64}}, typeof(DiffEqBase.ODE_DEFAULT_NORM), typeof(LinearAlgebra.opnorm), Bool, CallbackSet{Tuple{}, Tuple{}}, typeof(DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN), typeof(DiffEqBase.ODE_DEFAULT_PROG_MESSAGE), typeof(DiffEqBase.ODE_DEFAULT_UNSTABLE_CHECK), DataStructures.BinaryHeap{Float64, DataStructures.FasterForward}, DataStructures.BinaryHeap{Float64, DataStructures.FasterForward}, Nothing, Nothing, Float64, Tuple{}, Tuple{}, Tuple{}}, SVector{7, Float64}, Float64, Nothing, OrdinaryDiffEq.DefaultInit}, Vector{Float64}}, Vector{Float64}}, ChaosTools.var"#17#18"{typeof(jacob_HR_mem), Vector{Float64}}}, search::Type{IntervalRootFinding.DepthFirstSearch}, tol::Float64)
    @ IntervalRootFinding C:\Users\Alex\.julia\packages\IntervalRootFinding\gKaGR\src\roots.jl:86
 [19] _roots(f::Function, deriv::Function, r::IntervalRootFinding.Root{IntervalBox{7, Float64}}, contractor::Type{IntervalRootFinding.Krawczyk}, strategy::Type{IntervalRootFinding.DepthFirstSearch}, tol::Float64)
    @ IntervalRootFinding C:\Users\Alex\.julia\packages\IntervalRootFinding\gKaGR\src\roots.jl:184
 [20] _roots
    @ C:\Users\Alex\.julia\packages\IntervalRootFinding\gKaGR\src\roots.jl:198 [inlined]
 [21] roots(f::Function, deriv::Function, X::IntervalBox{7, Float64}, contractor::Type{IntervalRootFinding.Krawczyk}, tol::Float64)
    @ IntervalRootFinding C:\Users\Alex\.julia\packages\IntervalRootFinding\gKaGR\src\roots.jl:142
 [22] fixedpoints(ds::CoupledODEs{false, 7, OrdinaryDiffEq.ODEIntegrator{Vern9{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}, false, SVector{7, Float64}, Nothing, Float64, Vector{Float64}, Float64, Float64, Float64, Float64, Vector{SVector{7, Float64}}, ODESolution{Float64, 2, Vector{SVector{7, Float64}}, Nothing, Nothing, Vector{Float64}, Vector{Vector{SVector{7, Float64}}}, ODEProblem{SVector{7, Float64}, Tuple{Float64, Float64}, false, Vector{Float64}, ODEFunction{false, SciMLBase.AutoSpecialize, typeof(HR_mem), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, Vern9{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}, OrdinaryDiffEq.InterpolationData{ODEFunction{false, SciMLBase.AutoSpecialize, typeof(HR_mem), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, Vector{SVector{7, Float64}}, Vector{Float64}, Vector{Vector{SVector{7, Float64}}}, OrdinaryDiffEq.Vern9ConstantCache}, DiffEqBase.Stats, Nothing}, ODEFunction{false, SciMLBase.AutoSpecialize, typeof(HR_mem), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, OrdinaryDiffEq.Vern9ConstantCache, OrdinaryDiffEq.DEOptions{Float64, Float64, Float64, Float64, PIController{Rational{Int64}}, typeof(DiffEqBase.ODE_DEFAULT_NORM), typeof(LinearAlgebra.opnorm), Bool, CallbackSet{Tuple{}, Tuple{}}, typeof(DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN), typeof(DiffEqBase.ODE_DEFAULT_PROG_MESSAGE), typeof(DiffEqBase.ODE_DEFAULT_UNSTABLE_CHECK), DataStructures.BinaryHeap{Float64, DataStructures.FasterForward}, DataStructures.BinaryHeap{Float64, DataStructures.FasterForward}, Nothing, Nothing, Float64, Tuple{}, Tuple{}, Tuple{}}, SVector{7, Float64}, Float64, Nothing, OrdinaryDiffEq.DefaultInit}, Vector{Float64}}, box::IntervalBox{7, Float64}, J::Function; method::Type, tol::Float64, warn::Bool, o::Nothing)
    @ ChaosTools C:\Users\Alex\.julia\packages\ChaosTools\VMXUY\src\stability\fixedpoints.jl:60
 [23] fixedpoints(ds::CoupledODEs{false, 7, OrdinaryDiffEq.ODEIntegrator{Vern9{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}, false, SVector{7, Float64}, Nothing, Float64, Vector{Float64}, Float64, Float64, Float64, Float64, Vector{SVector{7, Float64}}, ODESolution{Float64, 2, Vector{SVector{7, Float64}}, Nothing, Nothing, Vector{Float64}, Vector{Vector{SVector{7, Float64}}}, ODEProblem{SVector{7, Float64}, Tuple{Float64, Float64}, false, Vector{Float64}, ODEFunction{false, SciMLBase.AutoSpecialize, typeof(HR_mem), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}}, SciMLBase.StandardODEProblem}, Vern9{typeof(OrdinaryDiffEq.trivial_limiter!), typeof(OrdinaryDiffEq.trivial_limiter!), Static.False}, OrdinaryDiffEq.InterpolationData{ODEFunction{false, SciMLBase.AutoSpecialize, typeof(HR_mem), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, Vector{SVector{7, Float64}}, Vector{Float64}, Vector{Vector{SVector{7, Float64}}}, OrdinaryDiffEq.Vern9ConstantCache}, DiffEqBase.Stats, Nothing}, ODEFunction{false, SciMLBase.AutoSpecialize, typeof(HR_mem), LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, Nothing}, OrdinaryDiffEq.Vern9ConstantCache, OrdinaryDiffEq.DEOptions{Float64, Float64, Float64, Float64, PIController{Rational{Int64}}, typeof(DiffEqBase.ODE_DEFAULT_NORM), typeof(LinearAlgebra.opnorm), Bool, CallbackSet{Tuple{}, Tuple{}}, typeof(DiffEqBase.ODE_DEFAULT_ISOUTOFDOMAIN), typeof(DiffEqBase.ODE_DEFAULT_PROG_MESSAGE), typeof(DiffEqBase.ODE_DEFAULT_UNSTABLE_CHECK), DataStructures.BinaryHeap{Float64, DataStructures.FasterForward}, DataStructures.BinaryHeap{Float64, DataStructures.FasterForward}, Nothing, Nothing, Float64, Tuple{}, Tuple{}, Tuple{}}, SVector{7, Float64}, Float64, Nothing, OrdinaryDiffEq.DefaultInit}, Vector{Float64}}, box::IntervalBox{7, Float64}, J::Function)
    @ ChaosTools C:\Users\Alex\.julia\packages\ChaosTools\VMXUY\src\stability\fixedpoints.jl:41
 [24] top-level scope
    @ c:\Users\Alex\Desktop\dynamical-systems\HIndmarsh Rose memristor\notebooks\timeseries phase pojections\Modes.ipynb:1

Earlier I tried to perform bifurcation analysis using matcont. In it, Newton’s method could not convergence to a state of equilibrium. The Jacobian is calculated correctly, I checked it with forwarddiff.

Thank you for your help

This means that the Jacobian matrix is singular and can’t be inverted, hence you can’t apply newton’s method to find fixed points. Use Attractors.jl instead.

1 Like

Thank you!