Waveform Stability Research Articles

Improved wave V resolution by dual-channel brain stem auditory evoked potential recording

Brain stem auditory evoked potentials were recorded simultaneously from the vertex and ear contralateral to stimulation (A c-C z) and from the vertex and ear ipsilateral to stimulation (A i-C z). There was clearer definition of wave V and less latency variability between trials in A c-C z channel recordings, resulting in enhanced wave form stability and greater reproducibility of wave I-V interpeak latencies. The clinical interpretation of dual-channel recordings is currently limited by the complexity of the auditory pathways, but the technique itself shows promise as a routine clinical procedure.

Stability of periodic travelling wave solutions with large spatial periods in reaction-diffusion systems

We consider a spatially homogeneous system of reaction-diffusion equation defined on the interval (−∞, ∞) of the one-dimensional spatial variable x. It is known that this equation has a one-parameter family of periodic travelling wave solutions Ψ( x + ct; c) if this equation has a spatially homogeneous periodic solution φ( t). The spatial period L( c) of the travelling wave solution satisfies L(c) c → T if c → +∞ , where c is the propagation speed and T is the period of φ( t). We prove that, in the case c > 0 is sufficiently large, Ψ( x + ct; c) is unstable if φ( t) is “strongly unstable” and Ψ( x + ct; c) is “marginally stable” if φ( t) is “strongly stable.” If the equation is defined on a finite interval [0, l] of the variable x with the periodic boundary conditions, we can obtain a more precise result regarding the stability of Ψ(x + c ̂ t; c ̂ ) , where c ̂ > 0 is a speed which satisfies l = mL( c ̂ ) for some positive integer m. We prove that this solution is asymptotically stable in the sense of waveform stability if c ̂ > 0 is sufficiently large and if φ( t) is “strongly stable.”

Existence and stability of local excitations in homogeneous neural fields

Dynamics of excitation patterns is studied in one-dimensional homogeneous lateral-inhibition type neural fields. The existence of a local excitation pattern solution as well as its waveform stability is proved by the use of the Schauder fixed-point theorem and a generalized version of the Perron-Frobenius theorem of positive matrices to the fuction space. The dynamcis of the field is in general multi-stable so that the field can keep short-term memory.

Waveform stability of a traveling high-field domain in a Gunn diode

We assume that a constant voltage is applied across a sample of a Gunn diode of finite length. When a periodic boundary condition is assumed, the dynamical behavior of the electric field within the sample is described by a nonlinear integral-partial differential equation. By using this equation, we can study the waveform stability of a traveling high-field domain of solitary-wave type which plays an essential role in the Gunn effect. We obtain simple criteria which the sample length and the applied voltage must satisfy for the existence and stability of the high-field domain. The stability analysis is carried out by using Liapunov's second method.

Reaction-diffusion equation describing morphogenesis I. waveform stability of stationary wave solutions in a one dimensional model

Turing's mathematical model of morphogenesis is described by a nonlinear reaction-diffusion equation. In this paper, we simplify the nonlinear reaction terms of the model in order to make the analysis easy. We obtain a sufficient condition for the existence of the “stationary wave solutions”. The waveform stability of these solutions is proved by the use of a Liapunov functional. We also synthesize an electrical circuit simulating the model.

Early averaged electroencephalic responses to clicks in neonates.

The early (approximately 8–50 msec latency) averaged electroencephalic responses (AER) to 55 dB HL clicks were elicited from ten normal newborns 36 to 72 hours after birth. Early components were observed in all ten babies with 512 clicks presented at 4.5/sec and 9.0/sec. Mean peak latencies in msec were: Po — 11, Na — 17, Pa — 28, Nb — 35, and Pb — 51. The neonates' early component waveforms closely resemble those of adults. The latency and waveform stability of the early components in neonates and adults support the belief in the primary auditory (lemniscal) system as the mediator of these responses. Furthermore, the repeatability of the early components of the AER makes them more reliable response indices than the late components (approximately 50–400 msec) for audiometry with neonates.

Neuristor analysis techniques for nonlinear distributed electronic systems

Neuristor propagation analysis techniques apply to a wide variety of nonlinear distributed electronic devices and wave propagation phenomena. This paper brings together and reviews these techniques. A specific example, the superconductive tunnel junction stripline, is modeled by a distributed equivalent circuit described by nonlinear parabolic partial differential equations. The neuristor pulse propagates at constant velocity with a fixed waveshape; mathematically, this reduces the partial differential equations to ordinary differential equations which are solved by phase-plane topology analysis. Poincaré's index rule and Bendixson's negative criterion prescribe the pulse velocity and waveform. Analytical results agree with experiment. Pulse waveform stability is studied using eigenfunction expansion of the perturbation equations and Lyapunov theory, but complete results are not obtained. Lyapunov theory provides estimates of excitation thresholds for launching a neuristor pulse, which are consistent with experiment. Determining the nature of pulse interactions may for some systems be accomplished using the Bäcklund transformation or perturbation series techniques, but generally requires complete computer solution of the dynamical equations.

Waveform stability on a nonlinear Klein-Gordon equation

The eigenfunction expansion technique recently introduced by Parmentier is used to discuss the stability of dynamic steady-state waves on a nonlinear Klein-Gordon equation. More precise statements concerning stability can be made than was possible with the averaged Lagrangian technique of Whitham.

Stability of Waveforms on Active Nonlinear Transmission Lines

Steady propagation on both the tapered RC \pm G and RLC \pm G nonlinear transmission lines is investigated and the existence of various types of neuristor waveforms demonstrated. A generalization of the direct method of Liapunov for distributed parameter systems is employed to determine the stability of the possible steady waveforms. It is shown that the criterion for waveform stability on such active nonlinear transmission lines is simply that the derivative of the steady waveform represents the minimum eigenvalue solution of the linearized perturbation equation.

Neuristor waveform stability analysis by Lyapunov's second method

Lyapunov's second method gives a sufficient condition for the asymptotic stability of a dynamic steady-state waveform on a nonlinear active transmission line. The result is consistent with that of an eigenfunction expansion technique.