Search results for " Hopf bifurcation"
showing 3 items of 3 documents
Modelling prey-predator interactions in Messina beachrock pools
2020
Abstract The Strait of Messina (Sicily, Italy) attracts the interest of marine ecologists for the presence of a large variety of habitat and mutually-interacting communities. Among them, beachrock formations, despite their wide geographic distribution, which also includes the Mediterranean area, have been poorly investigated from the biotic viewpoint. In this paper, the spatial and seasonal variability of benthic megafauna from the Messina microtidal beachrock is described. Combining in situ collected data (measurements of abiotic parameters and underwater visual census) with theoretical post-processing analyses (analysis of similarity percentages and cluster analysis), we deduced the possi…
Turing Instability and Pattern Formation for the Lengyel–Epstein System with Nonlinear Diffusion
2014
In this work we study the effect of density dependent nonlinear diffusion on pattern formation in the Lengyel---Epstein system. Via the linear stability analysis we determine both the Turing and the Hopf instability boundaries and we show how nonlinear diffusion intensifies the tendency to pattern formation; in particular, unlike the case of classical linear diffusion, the Turing instability can occur even when diffusion of the inhibitor is significantly slower than activator's one. In the Turing pattern region we perform the WNL multiple scales analysis to derive the equations for the amplitude of the stationary pattern, both in the supercritical and in the subcritical case. Moreover, we c…
Scenario of the Birth of Hidden Attractors in the Chua Circuit
2017
Recently it was shown that in the dynamical model of Chua circuit both the classical selfexcited and hidden chaotic attractors can be found. In this paper the dynamics of the Chua circuit is revisited. The scenario of the chaotic dynamics development and the birth of selfexcited and hidden attractors is studied. It is shown a pitchfork bifurcation in which a pair of symmetric attractors coexists and merges into one symmetric attractor through an attractormerging bifurcation and a splitting of a single attractor into two attractors. The scenario relating the subcritical Hopf bifurcation near equilibrium points and the birth of hidden attractors is discussed.