We give a complete classification of the phase portraits in Poincare´ disk for cubic polynomial systemsx˙=1−x−axy2,y˙=−by+axy2, R2 according with values its two parameters and b. These differential systems correspond to Gray-Scott model. Moreover we provide bifurcation diagram parameter plane (a,b) these systems.

We consider the problem of dynamic cavity formation in isotropic compressible nonlinear elastic media. For the equations of radial elasticity we construct self-similar weak solutions that describe a cavity emanating from a state of uniform deformation. For dimensions d = 2, 3 we show that cavity formation is necessarily associated with a unique precursor shock. We also study the bifurcation dia...

We study the effect of time delayed feedback control in the form proposed by Pyragas on deterministic chaos in the Rössler system. We reveal the general bifurcation diagram in the parameter plane of time delay tau and feedback strength K which allows one to explain the phenomena that have been discovered in some previous works. We show that the bifurcation diagram has essentially a multileaf st...

We explore different two-parametric families of quasi-periodically Forced Logistic Maps looking for universality and self-similarity properties. In the bifurcation diagram of the one-dimensional Logistic Map, it is well known that there exist parameter values sn where the 2-periodic orbit is superattracting. Moreover, these parameter values lay between the parameters corresponding to two consec...

We study the morphologies of single liquid droplets wetting a substrate in the presence of the line tension of the three-phase contact line. On a homogeneous substrate, the line tension leads to a discontinuous unbinding of the droplet if its volume is decreased below a critical value. For a droplet wetting a structured surface with a circular domain, a line tension contrast gives rise to disco...

Dynamics and digital circuit implementation of the fractional-order Lorenz system are investigated by employing Adomian decomposition method (ADM). Dynamics of the fractional-order Lorenz system with derivative order and parameter varying is analyzed by means of Lyapunov exponents (LEs), bifurcation diagram, chaos diagram and phase diagram. Results show that the fractional-order Lorenz system h...

In this paper we revisit the Mackey-Glass model for blood-forming process, which was proposed to describe the spontaneous fluctuations of the blood cell counts in normal individuals and the first stage of chronic myelocytic (or granylocytic) leukemia (CML). We obtain the bifurcation diagram as a function of the time delay parameter and show that the onset of leukemia is related to instabilities...