Aleph-w 3.0
A C++ Library for Data Structures and Algorithms
Loading...
Searching...
No Matches
Public Types | Public Member Functions | Private Member Functions | Private Attributes | List of all members
Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel > Class Template Reference

FitzHugh-Nagumo excitable-media rule. More...

#include <tpl_ca_continuous_rules.H>

Collaboration diagram for Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >:
[legend]

Public Types

using state_type = Reaction_Diffusion_Cell< Real >
 Cell state consumed and produced by the rule.
 
using kernel_type = Kernel
 Laplacian kernel type.
 

Public Member Functions

 FitzHugh_Nagumo_Rule (Real a, Real b, Real epsilon, Real du, Real dv, Real dt=Real{0.01}, Real stimulus=Real{}, Kernel laplacian=laplacian_5p_kernel< Real >())
 Build a FitzHugh-Nagumo rule.
 
Real a () const noexcept
 
Real b () const noexcept
 
Real epsilon () const noexcept
 
Real Du () const noexcept
 
Real Dv () const noexcept
 
Real dt () const noexcept
 
Real stimulus () const noexcept
 
const Kernel & laplacian () const noexcept
 
state_type operator() (const state_type &current, Neighbor_View< state_type > neighbours) const
 Compute the next FitzHugh-Nagumo state.
 

Private Member Functions

Real laplace_u (Neighbor_View< state_type > neighbours, const state_type &current) const
 
Real laplace_v (Neighbor_View< state_type > neighbours, const state_type &current) const
 

Private Attributes

Real a_
 
Real b_
 
Real epsilon_
 
Real du_
 
Real dv_
 
Real dt_
 
Real stimulus_
 
Kernel lap_
 

Detailed Description

template<typename Real = double, typename Kernel = Kernel2D<Real, 3, 3>>
class Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >

FitzHugh-Nagumo excitable-media rule.

Explicit Euler update:

du/dt = Du * Lap(u) + u - u^3 / 3 - v + stimulus
dv/dt = Dv * Lap(v) + epsilon * (u + a - b*v)
Aleph::CA::FitzHugh_Nagumo_Rule::Du
Real Du() const noexcept
Definition tpl_ca_continuous_rules.H:562
Aleph::CA::FitzHugh_Nagumo_Rule::dt
Real dt() const noexcept
Definition tpl_ca_continuous_rules.H:574
Aleph::CA::FitzHugh_Nagumo_Rule::a
Real a() const noexcept
Definition tpl_ca_continuous_rules.H:544
Aleph::CA::FitzHugh_Nagumo_Rule::stimulus
Real stimulus() const noexcept
Definition tpl_ca_continuous_rules.H:580
Aleph::CA::FitzHugh_Nagumo_Rule::epsilon
Real epsilon() const noexcept
Definition tpl_ca_continuous_rules.H:556
Aleph::CA::FitzHugh_Nagumo_Rule::b
Real b() const noexcept
Definition tpl_ca_continuous_rules.H:550
Aleph::CA::FitzHugh_Nagumo_Rule::Dv
Real Dv() const noexcept
Definition tpl_ca_continuous_rules.H:568
Aleph::blossom_maximum_cardinality_matching
size_t blossom_maximum_cardinality_matching(const GT &g, DynDlist< typename GT::Arc * > &matching, SA sa=SA())
Alias of compute_maximum_cardinality_general_matching().
Definition Blossom.H:466

The constructor enforces 0 < dt <= 0.25. This conservative bound keeps the explicit update stable for the usual tutorial parameters (a=0.7, b=0.8, epsilon=0.08, dt=0.01) and catches accidental blow-ups early.

Template Parameters
Realfloating-point field type.
KernelLaplacian kernel type.

Definition at line 467 of file tpl_ca_continuous_rules.H.

Member Typedef Documentation

◆ kernel_type

template<typename Real = double, typename Kernel = Kernel2D<Real, 3, 3>>
using Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::kernel_type = Kernel

Laplacian kernel type.

Definition at line 473 of file tpl_ca_continuous_rules.H.

◆ state_type

template<typename Real = double, typename Kernel = Kernel2D<Real, 3, 3>>
using Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::state_type = Reaction_Diffusion_Cell<Real>

Cell state consumed and produced by the rule.

Definition at line 471 of file tpl_ca_continuous_rules.H.

Constructor & Destructor Documentation

◆ FitzHugh_Nagumo_Rule()

template<typename Real = double, typename Kernel = Kernel2D<Real, 3, 3>>
Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::FitzHugh_Nagumo_Rule ( Real  a,
Real  b,
Real  epsilon,
Real  du,
Real  dv,
Real  dt = Real{0.01},
Real  stimulus = Real{},
Kernel  laplacian = laplacian_5p_kernel<Real>() 
)
inline

Build a FitzHugh-Nagumo rule.

Parameters
[in]arecovery nullcline offset.
[in]brecovery coupling coefficient; must be positive.
[in]epsilonrecovery time-scale parameter; must be positive.
[in]dudiffusion coefficient for u.
[in]dvdiffusion coefficient for v.
[in]dtexplicit Euler time step; stable contract: 0 < dt <= 0.25.
[in]stimulusconstant external stimulus added to u.
[in]laplacianconvolution kernel; defaults to 5-point Laplacian.
Exceptions
std::domain_errorif any parameter is outside its documented range.

Definition at line 517 of file tpl_ca_continuous_rules.H.

Member Function Documentation

◆ a()

template<typename Real = double, typename Kernel = Kernel2D<Real, 3, 3>>
Real Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::a ( ) const
inlinenoexcept
Returns
parameter a.

Definition at line 544 of file tpl_ca_continuous_rules.H.

References Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::a_.

◆ b()

template<typename Real = double, typename Kernel = Kernel2D<Real, 3, 3>>
Real Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::b ( ) const
inlinenoexcept
Returns
parameter b.

Definition at line 550 of file tpl_ca_continuous_rules.H.

References Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::b_.

◆ dt()

template<typename Real = double, typename Kernel = Kernel2D<Real, 3, 3>>
Real Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::dt ( ) const
inlinenoexcept
Returns
explicit Euler time step.

Definition at line 574 of file tpl_ca_continuous_rules.H.

References Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::dt_.

◆ Du()

template<typename Real = double, typename Kernel = Kernel2D<Real, 3, 3>>
Real Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::Du ( ) const
inlinenoexcept
Returns
u diffusion coefficient.

Definition at line 562 of file tpl_ca_continuous_rules.H.

References Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::du_.

◆ Dv()

template<typename Real = double, typename Kernel = Kernel2D<Real, 3, 3>>
Real Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::Dv ( ) const
inlinenoexcept
Returns
v diffusion coefficient.

Definition at line 568 of file tpl_ca_continuous_rules.H.

References Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::dv_.

◆ epsilon()

template<typename Real = double, typename Kernel = Kernel2D<Real, 3, 3>>
Real Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::epsilon ( ) const
inlinenoexcept
Returns
recovery time-scale parameter.

Definition at line 556 of file tpl_ca_continuous_rules.H.

References Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::epsilon_.

◆ laplace_u()

template<typename Real = double, typename Kernel = Kernel2D<Real, 3, 3>>
Real Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::laplace_u ( Neighbor_View< state_type >  neighbours,
const state_type &  current 
) const
inlineprivate

Definition at line 485 of file tpl_ca_continuous_rules.H.

References Aleph::blossom_maximum_cardinality_matching(), k, Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::lap_, and Aleph::CA::Reaction_Diffusion_Cell< Real >::u.

Referenced by Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::operator()().

◆ laplace_v()

template<typename Real = double, typename Kernel = Kernel2D<Real, 3, 3>>
Real Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::laplace_v ( Neighbor_View< state_type >  neighbours,
const state_type &  current 
) const
inlineprivate

Definition at line 493 of file tpl_ca_continuous_rules.H.

References Aleph::blossom_maximum_cardinality_matching(), k, Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::lap_, and Aleph::CA::Reaction_Diffusion_Cell< Real >::v.

Referenced by Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::operator()().

◆ laplacian()

template<typename Real = double, typename Kernel = Kernel2D<Real, 3, 3>>
const Kernel & Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::laplacian ( ) const
inlinenoexcept
Returns
Laplacian kernel.

Definition at line 586 of file tpl_ca_continuous_rules.H.

References Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::lap_.

◆ operator()()

template<typename Real = double, typename Kernel = Kernel2D<Real, 3, 3>>
state_type Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::operator() ( const state_type &  current,
Neighbor_View< state_type >  neighbours 
) const
inline

Compute the next FitzHugh-Nagumo state.

Parameters
[in]currentcurrent (u, v) fields.
[in]neighboursneighbour cells in Moore<2, Kernel::radius_v> order.
Returns
next field pair.
Exceptions
std::length_errorif neighbour count does not match the kernel.
std::runtime_errorif either field is non-finite or leaves [-100, 100], which signals numerical blow-up.

Definition at line 601 of file tpl_ca_continuous_rules.H.

References Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::a_, ah_length_error_if, Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::b_, Aleph::blossom_maximum_cardinality_matching(), Aleph::CA::ca_continuous_detail::checked_bounded(), Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::dt_, Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::du_, Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::dv_, Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::epsilon_, Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::laplace_u(), Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::laplace_v(), Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::stimulus_, Aleph::CA::Reaction_Diffusion_Cell< Real >::u, and Aleph::CA::Reaction_Diffusion_Cell< Real >::v.

◆ stimulus()

template<typename Real = double, typename Kernel = Kernel2D<Real, 3, 3>>
Real Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::stimulus ( ) const
inlinenoexcept
Returns
constant external stimulus.

Definition at line 580 of file tpl_ca_continuous_rules.H.

References Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::stimulus_.

Member Data Documentation

◆ a_

template<typename Real = double, typename Kernel = Kernel2D<Real, 3, 3>>
Real Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::a_
private

Definition at line 476 of file tpl_ca_continuous_rules.H.

Referenced by Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::a(), and Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::operator()().

◆ b_

template<typename Real = double, typename Kernel = Kernel2D<Real, 3, 3>>
Real Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::b_
private

Definition at line 477 of file tpl_ca_continuous_rules.H.

Referenced by Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::b(), and Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::operator()().

◆ dt_

template<typename Real = double, typename Kernel = Kernel2D<Real, 3, 3>>
Real Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::dt_
private

Definition at line 481 of file tpl_ca_continuous_rules.H.

Referenced by Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::dt(), and Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::operator()().

◆ du_

template<typename Real = double, typename Kernel = Kernel2D<Real, 3, 3>>
Real Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::du_
private

Definition at line 479 of file tpl_ca_continuous_rules.H.

Referenced by Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::Du(), and Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::operator()().

◆ dv_

template<typename Real = double, typename Kernel = Kernel2D<Real, 3, 3>>
Real Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::dv_
private

Definition at line 480 of file tpl_ca_continuous_rules.H.

Referenced by Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::Dv(), and Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::operator()().

◆ epsilon_

template<typename Real = double, typename Kernel = Kernel2D<Real, 3, 3>>
Real Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::epsilon_
private

Definition at line 478 of file tpl_ca_continuous_rules.H.

Referenced by Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::epsilon(), and Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::operator()().

◆ lap_

template<typename Real = double, typename Kernel = Kernel2D<Real, 3, 3>>
Kernel Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::lap_
private

Definition at line 483 of file tpl_ca_continuous_rules.H.

Referenced by Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::laplace_u(), Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::laplace_v(), and Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::laplacian().

◆ stimulus_

template<typename Real = double, typename Kernel = Kernel2D<Real, 3, 3>>
Real Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::stimulus_
private

Definition at line 482 of file tpl_ca_continuous_rules.H.

Referenced by Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::operator()(), and Aleph::CA::FitzHugh_Nagumo_Rule< Real, Kernel >::stimulus().

The documentation for this class was generated from the following file: