Basin stability approach for quantifying responses of multistable systems with parameters mismatch

Acknowledgement This work is funded by the National Science Center Poland based on the decision number DEC-2015/16/T/ST8/00516. PB is supported by the Foundation for Polish Science (FNP).Peer reviewedPublisher PD

Controlling multistability in coupled systems with soft impacts

This work has been supported by Lodz University of Technology own Scholarship Fund (PB) and by Stipend for Young Outstanding Scientists from Ministry of Science and Higher Education of Poland (PP). PB is supported by the Foundation for Polish Science (FNP).Peer reviewedPostprin

Erratum: Sample-based approach can outperform the classical dynamical analysis - experimental confirmation of the basin stability method

The original version of this Article contained a typographical error in the spelling of the author T. Kapitaniak, which was incorrectly given as T. Kapitaniakenglish. This has now been corrected in the PDF and HTML versions of the Article

Synchronous motion of two vertically excited planar elastic pendula

The dynamics of two planar elastic pendula mounted on the horizontally excited platform have been studied. We give evidence that the pendula can exhibit synchronous oscillatory and rotation motion and show that stable in-phase and anti-phase synchronous states always co-exist. The complete bifurcational scenario leading from synchronous to asynchronous motion is shown. We argue that our results are robust as they exist in the wide range of the system parameters.Comment: Submitte

Sample-based approach can outperform the classical dynamical analysis - Experimental confirmation of the basin stability method

In this paper we show the first broad experimental confirmation of the basin stability approach. The basin stability is one of the sample-based approach methods for analysis of the complex, multidimensional dynamical systems. We show that investigated method is a reliable tool for the analysis of dynamical systems and we prove that it has a significant advantages which make it appropriate for many applications in which classical analysis methods are difficult to apply. We study theoretically and experimentally the dynamics of a forced double pendulum. We examine the ranges of stability for nine different solutions of the system in a two parameter space, namely the amplitude and the frequency of excitation. We apply the path-following and the extended basin stability methods (Brzeski et al., Meccanica 51(11), 2016) and we verify obtained theoretical results in experimental investigations. Comparison of the presented results show that the sample-based approach offers comparable precision to the classical method of analysis. However, it is much simpler to apply and can be used despite the type of dynamical system and its dimensions. Moreover, the sample-based approach has some unique advantages and can be applied without the precise knowledge of parameter values

Dynamical response of a rocking rigid block

This is the author accepted manuscript. The final version is available from AIP Publishing via the DOI in this recordData accessibility: The data that support the findings of this study are available from the corresponding author upon reasonable request.This paper investigates the complex dynamical behavior of a rigid block structure under harmonic ground excitation, thereby mimicking, for instance, the oscillation of the system under seismic excitation or containers placed on a ship under periodic acting of sea waves. The equations of motion are derived assuming a large frictional coefficient at the interface between the block and the ground, in such a way that sliding cannot occur. In addition, the mathematical model assumes a loss of kinetic energy when an impact with the ground takes place. The resulting mathematical model is then formulated and studied in the framework of impulsive dynamical systems. Its complex dynamical response is studied in detail using two different approaches, based on direct numerical integration and path-following techniques, the latter implemented via the continuation platform COCO (Dankowicz & Schilder). Our study reveals the presence of various dynamical phenomena, such as branching points, fold and period-doubling bifurcation of limit cycles, symmetric and asymmetric periodic responses, as well as chaotic motion. By using basin stability method we also investigate the properties of solutions and their ranges of existence in phase and parameters spaces. Moreover, the study considers ground excitation conditions leading to the overturning of the block structure and shows parameters regions wherein such behavior can be avoidedEngineering and Physical Sciences Research Council (EPSRC)National Science Centre, Polan

DelayAndPeriodicity

Systems with time delay play an important role in modeling of many physical and biological processes. In this paper we describe generic properties of systems with time delay, which are related to the appearance and stability of periodic solutions. In particular, we show that delay systems generically have families of periodic solutions, which are reappearing for infinitely many delay times. As delay increases, the solution families overlap leading to increasing coexistence of multiple stable as well as unstable solutions. We also consider stability issue of periodic solutions with large delay by explaining asymptotic properties of the spectrum of characteristic multipliers. We show that the spectrum of multipliers can be splitted into two parts: pseudo-continuous and strongly unstable. The pseudo-continuous part of the spectrum mediates destabilization of periodic solutions.Comment: 24 pages, 9 figure

Periodic patterns in a ring of delay-coupled oscillators.

We describe the appearance and stability of spatiotemporal periodic patterns (rotating waves) in unidirectional rings of coupled oscillators with delayed couplings. We show how delays in the coupling lead to the splitting of each rotating wave into several new ones. The appearance of rotating waves is mediated by the Hopf bifurcations of the symmetric equilibrium. We also conclude that the coupling delays can be effectively replaced by increasing the number of oscillators in the chain. The phenomena are shown for the Stuart-Landau oscillators as well as for the coupled FitzHugh-Nagumo systems modeling an ensemble of spiking neurons interacting via excitatory chemical synapses

<Contributed Talk 9>HOW CHAOTIC (OR RANDOM) IS THE DICE THROW?

[Date] November 28 (Mon) - December 2 (Fri), 2011: [Place] Kyoto University Clock Tower Centennial Hall, Kyoto, JAPA