Eckhaus instability in systems with large delay

The dynamical behavior of various physical and biological systems under the influence of delayed feedback or coupling can be modeled by including terms with delayed arguments in the equations of motion. In particular, the case of long delay may lead to complicated and high-dimensional dynamics. We investigate the effects of delay in systems that display an oscillatory instability (Hopf bifurcation) in the absence of delay. We show by analytical and numerical methods that the dynamical scenario includes the coexistence of multiple stable periodic solutions and can be described in terms of the Eckhaus instability, which is well known in the context of spatially extended systems.     

Defect driven ferroelectricity and magnetism in nanocrystalline KTaO3

Nominally pure nanocrystalline KTaO₃ was thoroughly investigated by micro-Raman and magnetic resonance spectroscopic techniques. In all samples the defect driven ferroelectricity and magnetism are registered. Both ordering states are suggested to appear due to the iron atoms and oxygen vacancies. The concentration of defects was estimated to be 0.04 and 0.06-0.1 mol%. Note that undoped single crystals of KTaO₃ are nonmagnetic and have never exhibited ferromagnetic properties. The results enable us to refer a nanosized KTaO₃ to the class of multiferroics and assume that it could perform the magnetoelectric effect at T<29 K. It was also established that the critical concentration of impurity defects necessary to provoke the appearance of the new phase states in the material strongly correlates with the size of the particle; as the size of the particle decreases, the critical concentration decreases as well.     

Two-cluster bifurcations in systems of globally pulse-coupled oscillators

For a system of globally pulse-coupled phase-oscillators, we derive conditions for stability of the completely synchronous state and all stationary two-cluster states and explain how the different states are naturally connected via bifurcations. The coupling is modeled using the phase-response-curve (PRC), which measures the sensitivity of each oscillator’s phase to perturbations. For large systems with a PRC, which is zero at the spiking threshold, we are able to find the parameter regions where multiple stable two-cluster states coexist and illustrate this by an example. In addition, we explain how a locally unstable one-cluster state may form an attractor together with its homoclinic connections. This leads to the phenomenon of intermittent, asymptotic synchronization with abating beats away from the perfect synchrony.