We present the results of a theoretical investigation into the dynamics of a vibrating particle propelled by its self-induced wave field. Inspired by the hydrodynamic pilot-wave system discovered by Yves Couder and Emmanuel Fort, the idealized pilot-wave system considered here consists of a particle guided by the slope of its quasi-monochromatic "pilot" wave, which encodes the history of the particle motion. We characterize this idealized pilot-wave system in terms of two dimensionless groups that prescribe the relative importance of particle inertia, drag and wave forcing. Prior work has delineated regimes in which self-propulsion of the free particle leads to steady or oscillatory rectilinear motion; it has further revealed parameter regimes in which the particle executes a stable circular orbit, confined by its pilot wave. We here report a number of new dynamical states in which the free particle executes self-induced wobbling and precessing orbital motion. We also explore the statistics of the chaotic regime arising when the time scale of the wave decay is long relative to that of particle motion and characterize the diffusive and rotational nature of the resultant particle dynamics. We thus present a detailed characterization of free-particle motion in this rich two-parameter family of dynamical systems.A ring chain of the coupled Van der Pol equations with two types of unidirectional advective couplings is considered. It is assumed that the number of elements in the chain is sufficiently large. The transition to a distributed model with a continuous spatial variable is realized. We study the local-in the equilibrium neighborhood-dynamics of such a model. It is shown that the critical cases in the problem of the zero solution stability have infinite dimension.  https://www.selleckchem.com/products/icg-001.html  As the main result, the special nonlinear partial differential equations are constructed that do not contain small and large parameters, which are the equations of the first approximation their solutions determine the main part of the asymptotic behavior of the original model solutions. Thereby, the nonlocal dynamics of the constructed equations describes the local structure of the Van der Pol chain solutions. The asymptotic behavior of the solutions is carried out. Differences were revealed when using various unidirectional couplings. It is shown that these differences can be significant. In some of the most interesting cases, the obtained equations of the first approximation contain two spatial variables; therefore, it is natural to expect the appearance of complex dynamic effects. The studies are methodologically based on the method for constructing quasinormal forms developed by the author.With the rapid development of information technology, traditional infrastructure networks have evolved into cyber physical systems (CPSs). However, this evolution has brought along with it cyber failures, in addition to physical failures, which can affect the safe and stable operation of the whole system. In light of this, in this paper, we propose an interdependence-constrained optimization model to improve the robustness of the cyber physical system. The proposed model includes not only the realistic physical law but also the interdependence between the physical network and the cyber network. However, this model is highly nonlinear and cannot be solved directly. Therefore, we transform the model into a bi-level mixed integer linear programming problem, which can be easily and effectively solved in polynomial time. We conduct the simulation based on standard Institute of Electrical and Electronics Engineers test cases and study the impact of the disaster level and coupling strength on the robustness of the whole system. The simulation results show that our proposed model can effectively improve the robustness of the cyber physical system. Moreover, we compare the performance of the power supply in different CPSs, which have different network structures of the cyber network. Our work can provide useful instructions for system operators to improve the robustness of CPSs after extreme events happen in them.We study the evolution of the probability density of ensembles of iterates of the logistic map that advance toward and finally remain at attractors of representative dynamical regimes. We consider the mirror families of superstable attractors along the period-doubling cascade and of chaotic-band attractors along the inverse band-splitting cascade. We examine also their common aperiodic accumulation point. The iteration time progress of the densities of trajectories is determined via the action of the Frobenius-Perron (FP) operator. As a difference with the study of individual orbits, the analysis of ensembles of positions offers a viewpoint from which the nonlinear dynamical features of this iconic model can be better characterized in statistical-mechanical terms. The scaling of densities along the considered families of attractors conforms to a renormalization-group (RG) structure, while their entropies are seen to attain extrema at the fixed points of the RG flows. Additionally, this entropy as a function of the map control parameter displays the characteristic features of an equation of state of a thermal system undergoing a second-order phase transition. We discuss our results.We generalize the study of the noisy Kuramoto model, considered on a network of two interacting communities, to the case where the interaction strengths within and across communities are taken to be different in general. Using a geometric interpretation of the self-consistency equations developed in Paper I of this series as well as perturbation arguments, we are able to identify all solution boundaries in the phase diagram. This allows us to completely classify the phase diagram in the four-dimensional parameter space and identify all possible bifurcation points. Furthermore, we analyze the asymptotic behavior of the solution boundaries. To illustrate these results and the rich behavior of the model, we present phase diagrams for selected regions of the parameter space.Multilayer networks are the underlying structures of multiple real-world systems where we have more than one type of interaction/relation between nodes social, biological, computer, or communication, to name only a few. In many cases, they are helpful in modeling processes that happen on top of them, which leads to gaining more knowledge about these phenomena. One example of such a process is the spread of influence. Here, the members of a social system spread the influence across the network by contacting each other, sharing opinions or ideas, or-explicitly-by persuasion. Due to the importance of this process, researchers investigate which members of a social network should be chosen as initiators of influence spread to maximize the effect. In this work, we follow this direction and develop and evaluate the sequential seeding technique for multilayer networks. Until now, such techniques were evaluated only using simple one layer networks. The results show that sequential seeding in multilayer networks outperforms the traditional approach by increasing the coverage and allowing to save the seeding budget.