Abstract In this paper, we develop an optimized hybrid block method which is combined with a modified cubic B-spline method, for solving non-linear partial differential equations. particular, it will be applied three well-known problems, namely, the Burgers equation, Buckmaster equation and FitzHugh–Nagumo equation. Most of developed methods in literature equations have not focused on optimizin...

We consider a network of reaction diffusion systems of generalized FitzHugh-Nagumo type, where the cubic function is replaced by a polynomial function with odd degree. We deal with asymptotic behaviour and synchronization of the whole network. These results extend a previous work in which we considered particular systems of FitzHugh Nagumo type.

We consider a bistable reaction-diffusion system arising in the theory of phase transitions; it appears in several physical contexts such as thin magnetic films and the microphase separation in diblock copolymer melts. Mathematically it takes the form of an Allen-Cahn equation coupled to an elliptic equation. This system possesses a Lyapunov functional which represents the Gibbs free energy of ...

In this paper, the Exp -function method with the aid of symbolic computational system is used to obtain the exact travelling wave and solitary solutions of the Fitzhugh-Nagumo (FN), Modified Liouville equations and bi-directional Kaup-Kupershmidt (bKK) equation (sixth-order nonlinear equation). An attempt has been made to show the capabilities and wide-range applications of the Exp -function me...

The paper proposes a new mathematical FitzHugh—Nagumo model with memory, which describes the propagation of nerve impulse in membrane. consists an integro-differential equation initial conditions (the Cauchy problem). difference kernel (memory function) was chosen as power function so that it can be rewritten terms fractional derivative. For problem, explicit finite-difference scheme is constru...

At the end of Sect. 2.2 I state that, as input current I increases, the first Hopf bifurcation 3 occurring in the Fitzhugh-Nagumo (FN) equation is supercritical. This is incorrect. 4 For neurally-relevant values of the time constant ratio τv/τr ! 1, it is subcritical and 5 is preceded by a saddle-node bifurcation in which the stable limit cycle and an unstable 6 cycle appear, as in the full Hod...

Abstract We will introduce numerical methods for systems of ODEs by considering the celebrated FitzHugh-Nagumo model published FitzHugh [1] in 1961 and, independently, Nagumo et. al. [2] 1962. The is a system ordinary differential equations with two unknowns, and commonly used as simple action potentials excitable pacemaker cells.

A nonlinear electrical circuit is proposed as a basic cell for modeling FitzHugh-Nagumo neurons with a modified excitability. Depending on initial conditions and parameters experiments show various dynamics including stability with excitation, bistability and oscillations. Moreover, we present an electrical circuit which will be used to realize a unidirectional coupling between two cells, mimic...