known as Kolmogorov system, the derivatives are performed with respect to the time variable and F , G are two functions in the variables x and y. If F and G are linear (LotkaVolterraGause model), then it is well known that there is at most one critical point in the interior of the realistic quadrant (x > 0, y > 0), and there are no limit cycles [10,14,16]. There are many natural phenomena which...

For time-periodic dissipative and irreducible type-K competitive Kolmogorov systems, it is proved that there is a canonically defined countable family F of unordered, disjoint invariant sets with the property that, for every persistent trajectory whose ω-limit set is not a cycle, there exists a unique trajectory in some element of F such that these two trajectories are asymptotic and the corres...

In recent years there has been a growing interest in the study of the dynamics of stochastic populations. A key question in population biology is to understand the conditions under which populations coexist or go extinct. Theoretical and empirical studies have shown that coexistence can be facilitated or negated by both biotic interactions and environmental fluctuations. We study the dynamics o...

We study the global existence and uniqueness of weak solutions to kinetic Kolmogorov-Vicsek models that can be considered a non-local non-linear Fokker-Planck type equation describing the dynamics of individuals with orientational interaction. This model is derived from the discrete Couzin-Vicsek algorithm as mean-field limit [2, 9], which governs the interactions of stochastic agents moving wi...

We have examined the localization properties of quantum eigenstates for a system having mixed-type classical dynamics. Emphasis is given to the structure of eigenfunctions and the local spectral density of states. The nature of strongly localized eigenstates can be explained by considering the corresponding classical motion on the Kolmogorov-Arnold-Moser tori. The weak localization of nearly de...

We have proposed novel measures based on the Kolmogorov complexity for use in complex system behavior studies and time series analysis. We have considered background of the Kolmogorov complexity and also we have discussed meaning of the physical as well as other complexities. To get better insights into the complexity of complex systems and time series analysis we have introduced the three nove...