In this note our aim is to point out that certain inequalities for modified Bessel functions of the first and second kind, deduced recently by Laforgia and Natalini, are in fact equivalent to the corresponding Turán type inequalities for these functions. Moreover, we present some new Turán type inequalities for the aforementioned functions and we show that their product is decreasing as a funct...

Here we study how to control the dynamics of excitable systems by using the phase control technique. Excitable systems are relevant in neuronal dynamics and therefore this method might have important applications. We use the periodically driven FitzHugh–Nagumo (FHN) model, which displays both spiking and non-spiking behaviours in chaotic or periodic regimes. The phase control technique consists...

Article history: Received 21 September 2011 Received in revised form 20 December 2011 Accepted 5 January 2012 Available online 11 January 2012 Communicated by A.R. Bishop We investigate the feedback control of a periodically driven FitzHugh–Nagumo circuit (FHN), which displays both spiking and non-spiking behaviors in chaotic or periodic regimes. The simple high pass filter (washout filter) is ...

In this paper, we employ the exp(-?(x))-expansion method to find the exact traveling wave solutions involving parameters of nonlinear evolution equations Fitzhugh-Nagumo (FN) equation and Modified Liouville equation. When these parameters are taken to be special values, the solitary wave solutions are derived from the exact traveling wave solutions. It is shown that the proposed method provides...

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...

Travelling wave solutions for the FitzHugh-Nagumo equations have been proved to exist, by various authors, close to a certain singular limit of the equations. In this paper it is proved that these waves are stable relative to the full system of partial differential equations; that is, initial values near (in the sup norm) to the travelling wave lead to solutions that decay to some translate of ...

We study a reaction-diffusion evolution equation perturbed by a Gaussian noise. Here the leading operator is the infinitesimal generator of a C0-semigroup of strictly negative type, the nonlinear term has at most polynomial growth and is such that the whole system is dissipative. The corresponding Itô stochastic equation describes a process on a Hilbert space with dissipative nonlinear drift an...

The wavefront profile and the propagation velocity of waves in an experimentally observed Belousov–Zhabotinskii reaction are analyzed and a revised FitzHumgh–Nagumo (FHN) model of these systems is identified. The ratio between the excitation period and the recovery period, for a solitary wave is studied, and included within the model. Averaged traveling velocities at different spatial positions...

A controller-propagator system with a FitzHugh–Nagumo equation can be reduced to a free boundary problem when a layer parameter ” is equal to zero. We shall show the existence of solutions and the occurence of a Hopf bifurcation for this free boundary problem as the controlling parameter varies. c © 1999 Elsevier Science B.V. All rights reserved. AMS classi cation: primary 35R35; 35B32; seconda...

Chains of N FitzHugh–Nagumo oscillators with a gradient in natural frequencies and strong diffusive coupling are analyzed in this paper. We study the system’s dynamics in the limit of infinitely large coupling and then treat the case when the coupling is large but finite as a perturbation of the former case. In the large coupling limit, the 2N -dimensional phase space has an unexpected structur...