Biomedical subjects

Orazio Descalzi

Publications and source records attributed to Orazio Descalzi.

4 recordsLinked to original sources

PubMed2005

Stable stationary and breathing holes at the onset of a weakly inverted instability.

We show numerically different stable localized structures including stationary holes, moving holes, breathing holes, stationary and moving pulses in the one-dimensional subcritical complex Ginzburg-Landau equation with periodic boundary conditions, and using two classes of initial conditions. The coexistence between different types of stable solutions is summarized in a phase diagram. Stable breathing moving holes as well as breathing nonmoving holes have not been described before for dissipative pattern-forming systems including reaction-diffusion systems.

Journal Article↗

PubMed2005

Static, oscillating modulus, and moving pulses in the one-dimensional quintic complex Ginzburg-Landau equation: an analytical approach.

By means of a matching approach we study analytically the appearance of static and oscillating-modulus pulses in the one-dimensional quintic complex Ginzburg-Landau equation without nonlinear gradient terms. When considering nonlinear gradient terms the method enables us to calculate the velocities of the stable and unstable moving pulses. We focus on this equation since it represents a prototype envelope equation associated with the onset of an oscillatory instability near a weakly inverted bifurcation. The results obtained using the analytic approximation scheme are in good agreement with direct numerical simulations. The method is also useful in studying other localized structures like holes.

Journal Article↗

PubMed2004

Coexistence of stable particle and hole solutions for fixed parameter values in a simple reaction diffusion system.

We present a simple autocatalytic reaction-diffusion model for two variables, which shows for fixed parameter values the simultaneous stable coexistence of particle solutions as well of two types of hole solutions. The associated spatially homogeneous system is characterized by the coexistence of one stable fixed point and a stable limit cycle solution. We compare our results to other dissipative systems which have for fixed parameters either stable particle or stable hole solutions including the quintic complex Ginzburg-Landau equation and the envelope equation for optical bistability as well as other reaction-diffusion models.

Journal Article↗

PubMed2004

Analytical approach to localized structures in a simple reaction-diffusion system.

We study from an analytical point of view a simple reaction-diffusion model, which admits stable oscillating localized structures as a consequence of the coexistence between a stable limit cycle and a stable fixed point. Using a generalized matching approach we are able to find approximate analytical expressions for localized oscillating structures in this reaction-diffusion model capturing all the essential ingredients of these breathing particlelike solutions.

Diffusion↗