On stability of two degenerate reaction–diffusion systems

On the Stability of Properly–degenerate Hamiltonian Systems with two degrees of freedom∗

Properly degenerate nearly–integrable Hamiltonian systems with two degrees of freedom such that the “intermediate system” depend explicitly upon the angle–variable conjugated to the non–degenerate action–variable are considered and, in particular, model problems motivated by classical examples of Celestial Mechanics, are investigated. Under suitable “convexity” assumptions on the intermediate H...

Slowly varying control parameters, delayed bifurcations, and the stability of spikes in reactiondiffusion systems

We present three examples of delayed bifurcations for spike solutions of reaction-diffusion systems. The delay effect results as the system passes slowly from a stable to an unstable regime, and was previously analyzed in the context of ODE’s in [P.Mandel and T.Erneux, J.Stat.Phys 48(5-6) pp.1059-1070, 1987]. It was found that the instability would not be fully realized until the system had ent...

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators

On asymptotic stability of Weber fractional differential systems

In this article, we introduce the fractional differential systems in the sense of the Weber fractional derivatives and study the asymptotic stability of these systems. We present the stability regions and then compare the stability regions of fractional differential systems with the Riemann-Liouville and Weber fractional derivatives.

On asymptotic stability of Prabhakar fractional differential systems

In this article, we survey the asymptotic stability analysis of fractional differential systems with the Prabhakar fractional derivatives. We present the stability regions for these types of fractional differential systems. A brief comparison with the stability aspects of fractional differential systems in the sense of Riemann-Liouville fractional derivatives is also given.