Numerical Integration of Izhikevich and HH model neurons (Stewart and Bair 2009)

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The Parker-Sochacki method is a new technique for the numerical integration of differential equations applicable to many neuronal models. Using this method, the solution order can be adapted according to the local conditions at each time step, enabling adaptive error control without changing the integration timestep. We apply the Parker-Sochacki method to the Izhikevich ‘simple’ model and a Hodgkin-Huxley type neuron, comparing the results with those obtained using the Runge-Kutta and Bulirsch-Stoer methods.
1 . Stewart RD, Bair W (2009) Spiking neural network simulation: numerical integration with the Parker-Sochacki method. J Comput Neurosci 27:115-33 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Realistic Network;
Brain Region(s)/Organism:
Cell Type(s): Hodgkin-Huxley neuron;
Gap Junctions:
Receptor(s): AMPA; Glutamate;
Transmitter(s): Gaba; Glutamate;
Simulation Environment: C or C++ program; MATLAB;
Model Concept(s): Simplified Models; Detailed Neuronal Models; Methods;
Implementer(s): Stewart, Robert [Robert.Stewart at];
Search NeuronDB for information about:  AMPA; Glutamate; Gaba; Glutamate;
/*Header file to accompany tm_util.c*/
/*Written by Dr Robert Stewart for Stewart & Bair, 2009*/

#ifndef INC_TM_UTIL_H
#define INC_TM_UTIL_H
typedef unsigned int uint32; /*synonym for unsigned 32 bit integer*/

typedef struct {
	uint32 n; /*target neuron*/
	float w; 	/*weight*/
	uint32 i;	/*delay interval upgraded to 32 bit integer*/
} synapse;

typedef struct {
	double v;
	double n;
	double m;
	double h;
	double a;
	double b;
	double c;
	double d;
	double I;
	double g_ampa;
	double g_gaba;
	uint32 n_out;
} neuron_tm; 

void tm_derivs(double *, double *, double *);
void tm_first(double **, double **, double *);
void tm_iter(double **, double **, double *, int);

#endif /* INC_TM_UTIL_H */

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