The present paper deals with a problem of a ratio-dependent predator-prey model. The deterministic and stochastic behaviour of the model system around biologically feasible equilibria are studied. Conditions for which the deterministic model enter into Hopf-bifurcation are worked out. Stochastic stability of the system around positive interior equilibrium is studied. To substantiate our analytical findings numerical simulations are carried out for hypothetical set of parameter values.

The slow dynamics and concomitant memory ͑aging͒ effects seen in nanomagnetic systems are analyzed on the basis of two separate paradigms: superparamagnets and spin glasses. It is argued that in a large class of aging phenomena it suffices to invoke superparamagnetic relaxation of individual single domain particles but with a distribution of their sizes. Cases in which interactions and randomness are important in view of distinctive experimental signatures are also discussed.

We describe a numerical scheme for exactly simulating the heat current behavior in a quantum harmonic chain with self-consistent reservoirs. Numerically-exact results are compared to classical simulations and to the quantum behavior under the linear response approximation. In the classical limit or for small temperature biases our results coincide with previous calculations. At large bias and for low temperatures the quantum dynamics of the system fundamentally differs from the closeto-equilibrium behavior, revealing in particular the effect of thermal rectification for asymmetric chains. Since this effect is absent in the classical analog of our model, we conclude that in the quantum model studied here thermal rectification is a purely quantum phenomenon, rooted in the quantum statistics.

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