scholarly journals Collective vibrations of a hydrodynamic active lattice

2020 ◽  
Vol 476 (2239) ◽  
pp. 20200155 ◽  
Author(s):  
S. J. Thomson ◽  
M. Durey ◽  
R. R. Rosales
Keyword(s):  
Nonlinear Dynamical System ◽  
Bath Surface ◽  
Nonlinear Dynamical ◽  
Weakly Nonlinear ◽  
New Class ◽  
Subcritical Hopf Bifurcation ◽  
Geometrical Constraints ◽  
Non Local ◽  
Collective Vibrations ◽  
Spatio Temporal

Recent experiments show that quasi-one-dimensional lattices of self-propelled droplets exhibit collective instabilities in the form of out-of-phase oscillations and solitary-like waves. This hydrodynamic lattice is driven by the external forcing of a vertically vibrating fluid bath, which invokes a field of subcritical Faraday waves on the bath surface, mediating the spatio-temporal droplet coupling. By modelling the droplet lattice as a memory-endowed system with spatially non-local coupling, we herein rationalize the form and onset of instability in this new class of dynamical oscillator. We identify the memory-driven instability of the lattice as a function of the number of droplets, and determine equispaced lattice configurations precluded by geometrical constraints. Each memory-driven instability is then classified as either a super- or subcritical Hopf bifurcation via a systematic weakly nonlinear analysis, rationalizing experimental observations. We further discover a previously unreported symmetry-breaking instability, manifest as an oscillatory–rotary motion of the lattice. Numerical simulations support our findings and prompt further investigations of this nonlinear dynamical system.

Bifurcations and Chaos in an Experimental Based Quasi-Continuum Nonlinear Dynamical System for the ‘Clapper’ Nanoresonator

2007 ◽  
Author(s):  
O. Gottlieb ◽  
A. Gemintern ◽  
R. H. Blick
Keyword(s):  
Dynamical System ◽  
Nonlinear Dynamical System ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Field Equations ◽  
Bifurcation Structure ◽  
Nonlinear Dynamical ◽  
Spatio Temporal ◽  
Initial Boundary Value ◽  
Temporal Field

In this paper we formulate and numerically investigate an experimentally based quasi-continuum nonlinear initial-boundary-value problem for the three-field ‘Clapper’ nanoresonator that consistently incorporates the system geometric nonlinearity with nonlinear contributions of both magnetomotive and electrodynamic excitation. The spatio-temporal field equations are then reduced via symmetry and a modal projection to an equivalent quasiperiodically excited, low order, nonlinear dynamical system. The governing parameters of the resulting system are matched with the experimentally measured resonance conditions for small amplitude response. Numerical analysis reveals a complex bifurcation structure of torus doubling culminating with a chaotic strange attractor that exhibits similar features to that previously measured in the ‘Clapper’ experiment.

Nonlinear Dynamics of a Model of Interacting Waves in a Space with Partially Reflecting Boundaries

1998 ◽  
Vol 08 (05) ◽  
pp. 1033-1041
Author(s):  
Alexandr P. Chetverikov
Keyword(s):  
Nonlinear Dynamical System ◽  
Statistical Processing ◽  
Computer Experiments ◽  
Interaction Space ◽  
Temporal Behavior ◽  
Nonlinear Dynamical ◽  
Parametric Plane ◽  
Reflecting Boundaries ◽  
Spatio Temporal ◽  
The Waves

We investigate numerically the spatio-temporal behavior of a bounded distributed nonlinear dynamical system of finite length that describes the interaction of two one-dimensional waves. The nonlinear and dispersion properties of the waves and conditions at the boundaries of the interaction space correspond to a simple case, when the electromagnetic wave in a waveguide interacts with the wave in the flow of oscillating electrons. Typical spatial structures of the waves, their temporal behavior and bifurcational transitions in the parametric plane are examined on the basis of the qualitative analysis and statistical processing of the data of the computer experiments.

Prediction of Solutions of the Duffing System with Tuned Mass Damper

2020 ◽  
Vol 22 (4) ◽  
pp. 983-990
Author(s):  
Konrad Mnich
Keyword(s):  
Dynamical System ◽  
Duffing Oscillator ◽  
Probabilistic Approach ◽  
Nonlinear Dynamical System ◽  
Tuned Mass Damper ◽  
Nonlinear Dynamical ◽  
Duffing System ◽  
Mass Damper ◽  
Basin Stability ◽  
Stability Concept

AbstractIn this work we analyze the behavior of a nonlinear dynamical system using a probabilistic approach. We focus on the coexistence of solutions and we check how the changes in the parameters of excitation influence the dynamics of the system. For the demonstration we use the Duffing oscillator with the tuned mass absorber. We mention the numerous attractors present in such a system and describe how they were found with the method based on the basin stability concept.

scholarly journals Robust Tracker of Hybrid Microgrids by the Invariant-Ellipsoid Set

Electronics ◽  
2021 ◽  
Vol 10 (15) ◽  
pp. 1794
Author(s):  
Hilmy Awad ◽  
Ehab H. E. Bayoumi ◽  
Hisham M. Soliman ◽  
Michele De Santis
Keyword(s):  
Sliding Mode ◽  
Tracking Error ◽  
Nonlinear Dynamical System ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Nonlinear Dynamical ◽  
Load Variations ◽  
Invariant Ellipsoid ◽  
Steady State Responses ◽  
Linearized Model

This paper introduces a new ellipsoidal-based tracker design to control a grid-connected hybrid direct current/alternating current (DC/AC) microgrid (MG). The proposed controller is robust against both parameters and load variations. The studied hybrid MG is modelled as a nonlinear dynamical system. A linearized model around an operating point is developed. The parameter changes are modelled as norm-bounded uncertainties. We apply the new extended version of the attractive (or invariant) ellipsoid for this tracking problem. Convex optimization is used to obtain the region’s minimal size where the tracking error between the state trajectories and the reference states converges. The sufficient conditions for stability are derived and solved based on linear matrix inequalities (LMIs). The proposed controller’s validity is shown via simulating the hybrid MG with various operational scenarios. In each scenario, the performance of the controller is compared with a recently proposed sliding mode controller. The comparison clearly illustrates the superiority of the developed controller in terms of transient and steady-state responses.

scholarly journals Spatio-temporal integration in plant tropisms

2019 ◽  
Vol 16 (154) ◽  
pp. 20190038 ◽  
Author(s):  
Yasmine Meroz ◽  
Renaud Bastien ◽  
L. Mahadevan
Keyword(s):  
Response Function ◽  
Shoot Growth ◽  
Analytic Solution ◽  
Temporal Integration ◽  
Time Varying ◽  
Local Response ◽  
History Of ◽  
Non Local ◽  
Spatio Temporal ◽  
Plant Shoots

Tropisms, growth-driven responses to environmental stimuli, cause plant organs to respond in space and time and reorient themselves. Classical experiments from nearly a century ago reveal that plant shoots respond to the integrated history of light and gravity stimuli rather than just responding instantaneously. We introduce a temporally non-local response function for the dynamics of shoot growth formulated as an integro-differential equation whose solution allows us to qualitatively reproduce experimental observations associated with intermittent and unsteady stimuli. Furthermore, an analytic solution for the case of a pulse stimulus expresses the response function as a function of experimentally tractable variables, which we calculate for the case of the phototropic response of Arabidopsis hypocotyls. All together, our model enables us to predict tropic responses to time-varying stimuli, manifested in temporal integration phenomena, and sets the stage for the incorporation of additional effects such as multiple stimuli, gravitational sagging, etc.

scholarly journals Complex partial synchronization patterns in networks of delay-coupled neurons

2019 ◽  
Vol 377 (2153) ◽  
pp. 20180128 ◽  
Author(s):  
D. Nikitin ◽  
I. Omelchenko ◽  
A. Zakharova ◽  
M. Avetyan ◽  
A. L. Fradkov ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Temporal Dynamics ◽  
Delay Systems ◽  
Theme Issue ◽  
Partial Synchronization ◽  
Multiplex Network ◽  
Control Scheme ◽  
Non Local ◽  
Spatio Temporal ◽  
Fast Oscillations

We study the spatio-temporal dynamics of a multiplex network of delay-coupled FitzHugh–Nagumo oscillators with non-local and fractal connectivities. Apart from chimera states, a new regime of coexistence of slow and fast oscillations is found. An analytical explanation for the emergence of such coexisting partial synchronization patterns is given. Furthermore, we propose a control scheme for the number of fast and slow neurons in each layer. This article is part of the theme issue ‘Nonlinear dynamics of delay systems’.

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