Controlling spatiotemporal chaos in chains of dissipative Kapitza pendula

Chacón, Ricardo; Marcheggiani, Laura

doi:10.1103/physreve.82.016201

Cited by 9 publications

(3 citation statements)

References 47 publications

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“…Of late, the understanding of periodically driven systems has become one of the most active areas of research in many body physics. In the context of spatiotemporal chaos, coupled Kapitza pendulum in a dissipative environment has been investigated in [15]. Ref.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a system of coupled inverted pendula with vertical forcing

Bhadra¹

2018

Preprint

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Dynamical stabilization of an inverted pendulum through vertical movement of the pivot is a well-known counter intuitive phenomenon in classical mechanics. This system is also known as Kapitza pendulum and the stability can be explained with the aid of effective potential. We explore the effect of many body interaction for such a system. Our numerical analysis shows that interaction between pendula generally degrades the dynamical stability of each pendulum. This effect is more pronounced in nearest neighbour coupling than all-to-all coupling and stability improves with the increase of the system size. We report development of beats and clustering in network of coupled pendula.

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Section: Introductionmentioning

confidence: 99%

Dynamics of a system of coupled inverted pendula with vertical forcing

Bhadra¹

2018

Preprint

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“…In the last two decades, many chaos control and chaos synchronization techniques, for example, the Ott, Grebogi, and Yorke (OGY) method [11], adaptive control [12,13], non-feedback control [14,15], open-plus-closed-loop (OPCL) control [16], self controlling feedback [17], threshold control [18] etc for controlling chaos and [19][20][21][22] etc for the synchronization of chaos have been developed. There are many other chaos control and synchronization mechanisms [23][24][25][26][27][28]. In the OGY method, the chaotic trajectories in the vicinity of unstable fixed points or unstable periodic orbits are stabilized using small perturbations.…”

Section: Introductionmentioning

confidence: 99%

Properties of threshold coupled bistable maps

Nag¹,

Poria²

2014

Phys. Scr.

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In this paper we have studied the spatiotemporal behaviour of threshold coupled bistable chaotic maps. We have shown the existence of various cycles of the single map with the variation of threshold value for fixed relaxation time. The effects of variation of relaxation time on the network of threshold coupled maps are presented for different threshold values. Excess propagation through open boundaries is calculated numerically. For a network of three threshold coupled maps, the propagation of excess through open boundaries is calculated analytically. The condition for the existence of the steady state profile of the excess is calculated. The effects of random coupling on spatiotemporal synchronization of the network of threshold coupled maps are investigated. The key observation is that threshold coupling provides an annihilation method of the coexisting chaotic attractors of the local map and stabilizes it to some fixed point or periodic attractor.

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“…The interesting physical behavior of Kapita's stable inverted pendulum has enticed several researchers to study the nonlinear case both experimentally [21][22][23] and numerically 22,[24][25][26][27][28][29] . For systems composed of particles in a STP potential, only a small number of publications have examined the nonlinear multiple particle dynamics accounting for the multi-particle interactions.…”

Section: Introductionmentioning

confidence: 99%

Computational studies of multiple-particle nonlinear dynamics in a spatio-temporally periodic potential

Myers

Marshall

et al. 2014

Journal of Applied Physics

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The spatio-temporally periodic (STP) potential is interesting in Physics due to the intimate coupling between its time and spatial components. In this paper, we begin with a brief discussion of the dynamical behaviors of a single particle in a STP potential and then examine the dynamics of multiple particles interacting in a STP potential via the electric Coulomb potential. For the multiple particles' case, we focus on the occurrence of bifurcations when the amplitude of the STP potential varies. It is found that the particle concentration of the system plays an important role; the type of bifurcations that occur and the number of attractors present in the Poincar e sections depend on whether the number of particles in the simulation is even or odd. In addition to the nonlinear dynamical approach, we also discuss dependence of the squared fractional deviation of particles' kinetic energy of the multiple particle system on the amplitude of the STP potential which can be used to elucidate certain transitions of states; this approach is simple and useful particularly for experimental studies of complicated interacting systems. V C 2014 AIP Publishing LLC.

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Controlling spatiotemporal chaos in chains of dissipative Kapitza pendula

Cited by 9 publications

References 47 publications

Dynamics of a system of coupled inverted pendula with vertical forcing

Dynamics of a system of coupled inverted pendula with vertical forcing

Properties of threshold coupled bistable maps

Computational studies of multiple-particle nonlinear dynamics in a spatio-temporally periodic potential

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