The influence of a tangential displacement on the strength of the adhesive contacts between gradient materials with different gradings of their properties has been studied. Variants with a controlled force (fixed load) and a controlled displacement (fixed grips) are considered. A relationship between the normal and tangential critical force components at which the contact is destroyed is obtained. It is valid within the whole interval of the gradient parameters, where the detachment criterium is obeyed. The optimal parameters at which the adhesive contact strength is maximum are determined. A case of detachment under the action of only the tangential force, i.e. when the normal force equals zero, is analyzed separately.

The Lorentz system of equations, in which gradient terms are taken into account, has been solved numerically. Three fundamentally different modes of evolution are considered. In the first mode, the spatial distribution of the order parameter permanently changes in time, and domains of two types with positive and negative order parameter values are formed. In the second mode, the order parameter distribution is close to the stationary one. Finally, in the third mode, the order parameter is identical over the whole space. The dependences of the average area of domains, their number, and their total area on the time are calculated in the first two cases. In the third case, the contribution of gradient terms completely vanishes, and a classical Lorenz attractor is realized.