# 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] đť’¦(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}, Î±::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, Newtonâ€™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 canâ€™t be inverted, hence you canâ€™t apply newtonâ€™s method to find fixed points. Use Attractors.jl instead.

1 Like

Thank you!