Hidden attractors in fundamental problems and engineering models

Recently a concept of self-excited and hidden attractors was suggested: an attractor is called a self-excited attractor if its basin of attraction overlaps with neighborhood of an equilibrium, otherwise it is called a hidden attractor. For example, hidden attractors are attractors in systems with no equilibria or with only one stable equilibrium (a special case of multistability and coexistence of attractors). While coexisting self-excited attractors can be found using the standard computational procedure, there is no standard way of predicting the existence or coexistence of hidden attractors in a system. In this plenary survey lecture the concept of self-excited and hidden attractors is discussed, and various corresponding examples of self-excited and hidden attractors are considered

Theory of differential inclusions and its application in mechanics

The following chapter deals with systems of differential equations with discontinuous right-hand sides. The key question is how to define the solutions of such systems. The most adequate approach is to treat discontinuous systems as systems with multivalued right-hand sides (differential inclusions). In this work three well-known definitions of solution of discontinuous system are considered. We will demonstrate the difference between these definitions and their application to different mechanical problems. Mathematical models of drilling systems with discontinuous friction torque characteristics are considered. Here, opposite to classical Coulomb symmetric friction law, the friction torque characteristic is asymmetrical. Problem of sudden load change is studied. Analytical methods of investigation of systems with such asymmetrical friction based on the use of Lyapunov functions are demonstrated. The Watt governor and Chua system are considered to show different aspects of computer modeling of discontinuous systems

Software defined networking challenges and future direction: A case study of implementing SDN features on OpenStack private cloud

Cloud computing provides services on demand instantly, such as access to network infrastructure consisting of computing hardware, operating systems, network storage, database and applications. Network usage and demands are growing at a very fast rate and to meet the current requirements, there is a need for automatic infrastructure scaling. Traditional networks are difficult to automate because of the distributed nature of their decision making process for switching or routing which are collocated on the same device. Managing complex environments using traditional networks is time-consuming and expensive, especially in the case of generating virtual machines, migration and network configuration. To mitigate the challenges, network operations require efficient, flexible, agile and scalable software defined networks (SDN). This paper discuss various issues in SDN and suggests how to mitigate the network management related issues. A private cloud prototype test bed was setup to implement the SDN on the OpenStack platform to test and evaluate the various network performances provided by the various configurations

Rare and hidden attractors in Van der Pol-Duffing oscillators

We study the dynamics of the single and coupled van der Pol-Duffing oscillators. Each oscillator is characterized by the multistability (the coexistence of attractors). Some of the coexisting attractors have very small basins of attraction (the rare ones) and some of them do not contain equilibria in their basin of attraction (the hidden ones). We perform the detailed bifurcation analysis of these attractors and investigate how this plethora of states influences the dynamics of the network of coupled oscillators. We have observed the cluster synchronization on different attractors as well as different types of chimera states

New topological tool for multistable dynamical systems

We introduce a new method for investigation of dynamical systems which allows us to extract as much information as possible about potential system dynamics, based only on the form of equations describing it. The discussed tool of critical surfaces, defined by the zero velocity (and/or) acceleration field for particular variables of the system is related to the geometry of the attractors. Particularly, the developed method provides a new and simple procedure allowing to localize hidden oscillations. Our approach is based on the dimension reduction of the searched area in the phase space and has an advantage (in terms of complexity) over standard procedures for investigating full-dimensional space. The two approaches have been compared using typical examples of oscillators with hidden states. Our topological tool allows us not only to develop alternate ways of extracting information from the equations of motion of the dynamical system, but also provides a better understanding of attractors geometry and their capturing in complex cases, especially including multistable and hidden attractors. We believe that the introduced method can be widely used in the studies of dynamical systems and their applications in science and engineering

Theorem and observation about the nature of perpetual points in conservative mechanical systems

Perpetual points have been defined recently and they have been associated with hidden attractors. The significance of these points for the dynamics of a system is ongoing research. Herein, a theorem is presented, describing the nature of the perpetual points in linear natural conservative mechanical systems and as it is shown they are defining the rigid body motions and vice versa. Subsequently, the perpetual points of two conservative nonlinear mechanical systems are determined. The first one is a two degrees of freedom nonlinear natural mechanical system and, as it is shown there are two sets of perpetual points which are associated with the rig-id body motions. The other system is a non-natural conservative system, a flexible spinning shaft with non-constant rotating speed and, as it is shown, there are also three sets of perpetual points, and all of them are associated with the rigid body motions. In all examined nonlinear systems, the same observation made, that the perpetual points are associated with the rigid body motions, but formal proofs with the associated conditions as future work should be considered to generalise this observation. This work is essential to understand the nature of perpetual points in mechanical systems and opens new horizons for new operational modes and new design processes, targeting the ultimate operational modes of many mechanical systems which are the rigid body motions without having any vibrations

Decentralized In-Network Management for the Future Internet

In-network management (INM) is a new paradigm for the management of the future Internet that is based on the principles of decentralization and self-organization. Its goal is to overcome the limitations of traditional network management and to achieve scalable and robust management systems with low complexity for large-scale, dynamic network environments. In this paper, we describe a framework for INM that provides a systematic approach to the embedding of management algorithms within the elements of a communication networks. In addition, we demonstrate the benefits of decentralized management in the context of two key management functions, namely real-time monitoring and event handling.</p