Coupling multistable systems : uncertainty due to the initial positions on the attractors

Acknowledgment This work has been supported by the Foundation for Polish Science, Team Programme – Project No. TEAM/2010/5/5.Peer reviewedPublisher PD

Coupling multistable systems: uncertainly due to the initial positions on the attractors.

We consider the coupling of multistable nonidentical systems. For small values of the coupling coefficient the behavior of the coupled system strongly depends on the actual position of trajectories on their attractors in the moment when the coupling is introduced. After reaching the coupling threshold value, this dependence disappears. We give an evidence that this behavior is robust as it exists for a wide range of parameters and different types of coupling. We argue why this behavior cannot be considered as a dependence on the initial conditions

The dynamics of the pendulum suspended on the forced Duffing oscillator

We investigate the dynamics of the pendulum suspended on the forced Duffing oscillator. The detailed bifurcation analysis in two parameter space (amplitude and frequency of excitation) which presents both oscillating and rotating periodic solutions of the pendulum has been performed. We identify the areas with low number of coexisting attractors in the parameter space as the coexistence of different attractors has a significant impact on the practical usage of the proposed system as a tuned mass absorber.Comment: Accepte

Optimization of the Control System Parameters with Use of the New Simple Method of the Largest Lyapunov Exponent Estimation.

This text covers application of Largest Lapunov Exponent (LLE) as a criterion for control performance assessment (CPA) in a simulated control system. The main task is to find a simple and effective method to search for the best configuration of a controller in a control system. In this context, CPA criterion based on calculation of LLE by means of a new method [3] is compared to classical CPA criteria used in control engineering [1]. Introduction contains references to previous publications on Lyapunov stability. Later on, description of classical criteria for CPA along with formulae is presented. Significance of LLE in control systems is explained. Moreover, new efficient formula for calculation of LLE [3] is shown. In the second part simulation of the control system used for experiment is described. The next part contains results of the simulation in which typical criteria for CPA are compared with criterion based on value of LLE. In the last part results of the experiment are summed up and conclusions are drawn

The dynamics of co- and counter rotating coupled spherical pendulums

The dynamics of co- and counter-rotating coupled spherical pendulums (two lower pendulums are mounted at the end of the upper pendulum) is considered. Linear mode analysis shows the existence of three rotating modes. Starting from linear modes allow we calculate the nonlinear normal modes, which are and present them in frequency-energy plots. With the increase of energy in one mode we observe a symmetry breaking pitchfork bifurcation. In the second part of the paper we consider energy transfer between pendulums having different energies. The results for co-rotating (all pendulums rotate in the same direction) and counter-rotating motion (one of lower pendulums rotates in the opposite direction) are presented. In general, the energy fluctuations in counter-rotating pendulums are found to be higher than in the co-rotating case.Comment: The European Physical Journal Special Topics 201

State Dependent Delayed Drill-string Vibration : Theory, Experiments and New Model

L.J. Pei would like to acknowledge NNSF of China (No. 11372282) and China Scholarship Council.Peer reviewedPublisher PD

Lag Synchronization in Coupled Multistable van der Pol-Duffing Oscillators

We consider the system of externally excited identical van der Pol-Duffing oscillators unidirectionally coupled in a ring. When the coupling is introduced, each of the oscillator’s trajectories is on different attractor. We study the changes in the dynamics due to the increase in the coupling coefficient. Studying the phase of the oscillators, we calculate the parameter value for which we obtain the antiphase lag synchronization of the system and also the bifurcation values for which we observe qualitative changes in the dynamics of already synchronized system. We give evidence that lag synchronization is typical for coupled multistable systems

Different types of chimera states: An interplay between spatial and dynamical chaos

We discuss the occurrence of chimera states in networks of nonlocally coupled bistable oscillators, in which individual subsystems are characterized by the coexistence of regular (a fixed point or a limit cycle) and chaotic attractors. By analyzing the dependence of the network dynamics on the range and strength of coupling, we identify parameter regions for various chimera states, which are characterized by different types of chaotic behavior at the incoherent interval. Besides previously observed chimeras with space-temporal and spatial chaos in the incoherent intervals we observe another type of chimera state in which the incoherent interval is characterized by a central interval with standard space-temporal chaos and two narrow side intervals with spatial chaos. Our findings for the maps as well as for time-continuous van der Pol–Duffing’s oscillators reveal that this type of chimera states represents characteristic spatiotemporal patterns at the transition from coherence to incoherence

Synchronization in Coupled Multistable Systems with Hidden Attractors

In this paper, we study the results of coupling multistable systems which have hidden attractors with each other. Three modified Sprott systems were coupled and their synchronization was observed. The final state of the synchronized system changes with the change in the coupling strength. This was seen for two different types of coupling, one with a single variable and the other with two system variables