V. CONCLUSION. First let us discuss one possible generalization of our approach for the problem of interest not considered here. The concrete calculations here have been done for the most symmetric configurations of the system; namely the ideal square lattice array, and individual dots having rotational uniaxial symmetry. The consideration of the same problem with lower symmetry will not produce any principal difficulties. For a lattice of lower symmetry, such as rectangular, the same peculiarities for dipolar sums and long wave asymptotics of dispersion relations are present. The case of dots of lower symmetry, such as rectangular or elliptic, with almost homogeneous magnetization within the dots can be easily analyzed, just by adding to Eq. (1) extra terms describing more complicated (biaxial) anisotropy of a single dot. Qualitatively the results will be the same. In conclusion, the dynamic properties of the array of magnetic dots of different types without direct exchange interaction between dots have been investigated. For such systems, only the magnetic dipole interaction can be a source of dot interaction. Exploiting the translation symmetry of the array, and by use of the quasiparticle (magnon) formalism, we have found full spectra for the change of quasimomentum within all of the Brillouin zone. The direct measurement of the dependence ω ( ⃗ k ) can be done by the Brillouin light scattering method. Our calculations demonstrate that the dispersion is a strongly increasing function of the dot thickness. It will be interesting to observe non-monotonic dependence ω ( ⃗ k ) and especially, the change of the character of this dependence with the change of the magnetic field found here. The most impressive change of the ω ( ⃗ k ) dependence should appears near the transition from the FM to AFM states of an array. This property can be of interest for the design of a new generation of microwave devices in the modern direction of the applied physics of magnetic nanoparticles, i.e., the so-called magnonics, which has been widely discussed in the literature. 40 An important application of the calculated dispersion laws is the investigation of the stability of given magnetic states of the array. It has been found that for arrays with homogeneous magnetization within a dot directed perpendicular to the array’s plane there will always be a nonzero critical field, either external or in combination with an anisotropy field. For ferromagnetic state of array, the instability is developed for the quasimomentum at the points of the type of (1,0) at the border of the Brillouin zone, and it leads to a transition 23