Erratum: Bifurcation threshold of the delayed van der Pol oscillator under stochastic modulation [Phys. Rev. E 85, 056214 (2012)].

This corrects the article DOI: 10.1103/PhysRevE.85.056214.

Filtration, adsorption and immunodetection of virus using polyelectrolyte multilayer-modified paper.

A new method for detection of viruses has been developed. The entire assay can be performed within 2h, and consists of a polyelectrolyte-multilayer-modified cellulosic filter paper combined with immunodetection. The M13 bacteriophage was used as a model virus. A visual colour-based detection system, anti-M13 horseradish peroxidase (HRP) conjugate and 3,3',5,5'-tetramethylbenzidine (TMB), was selected to allow semi-quantitative assessment by human eye, or quantitative assessment using a digital scanner. By filtering a volume of 0.50 ml, it was possible to visually detect a concentration of 10(6) pfu/ml. The detection limit was improved to 5×10(4) pfu/ml by increasing the volume of the sample to 100ml. For comparison, it was only possible to detect a concentration of 10(7) pfu/ml using conventional sandwich enzyme-linked immunosorbent assay (ELISA) with the same detection system.

Bifurcation threshold of the delayed van der Pol oscillator under stochastic modulation.

We obtain the location of the Hopf bifurcation threshold for a modified van der Pol oscillator, parametrically driven by a stochastic source and including delayed feedback in both position and velocity. We introduce a multiple scale expansion near threshold, and we solve the resulting Fokker-Planck equation associated with the evolution at the slowest time scale. The analytical results are compared with a direct numerical integration of the model equation. Delay modifies the Hopf frequency at threshold and leads to a stochastic bifurcation that is shifted relative to the deterministic limit by an amount that depends on the delay time, the amplitude of the feedback terms, and the intensity of the noise. Interestingly, stochasticity generally increases the region of stability of the limit cycle.

Analytical determination of the bifurcation thresholds in stochastic differential equations with delayed feedback.

Analytical expressions for pitchfork and Hopf bifurcation thresholds are given for a nonlinear stochastic differential delay equation with feedback. Our results assume that the delay time τ is small compared to other characteristic time scales, not a significant limitation close to the bifurcation line. A pitchfork bifurcation line is found, the location of which depends on the conditional average , where x(t) is the dynamical variable. This conditional probability incorporates the combined effect of fluctuation correlations and delayed feedback. We also find a Hopf bifurcation line which is obtained by a multiple scale expansion around the oscillatory solution near threshold. We solve the Fokker-Planck equation associated with the slowly varying amplitudes and use it to determine the threshold location. In both cases, the predicted bifurcation lines are in excellent agreement with a direct numerical integration of the governing equations. Contrary to the known case involving no delayed feedback, we show that the stochastic bifurcation lines are shifted relative to the deterministic limit and hence that the interaction between fluctuation correlations and delay affect the stability of the solutions of the model equation studied.