Traveling chimera states for coupled pendula

Dudkowski, Dawid; Czołczyński, Krzysztof; Kapitaniak, Tomasz

doi:10.1007/s11071-018-4664-5

Cited by 34 publications

(14 citation statements)

References 30 publications

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“…The theory of dynamical systems is one of the most commonly used keys to solve and understand modern problems occurring in physics, chemistry, biology, and other natural sciences. However, a large variety of mechanical systems composed of a pendulum [32][33][34] or of several coupled pendula [35,36] commonly offer a synchronous dynamics. These dynamics might benefit the structure connected to those pendula in terms of reducing the amplitude of vibration.…”

Section: Stability Analysis Of the Systemmentioning

confidence: 99%

On Appearance of Fast or Late Self-Synchronization between Non-Ideal Sources Mounted on a Rectangular Plate Due to Time Delay

Djanan

Marburg

Nbendjo

2022

MCA

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The present paper aims to present the effects of late switching on (time delay) between two or three DC electrical machines characterized by limited power supplies on their fast or late self-synchronization when mounted on a rectangular plate with simply supported edges. The DC electrical machines are considered here as non-ideal oscillators, rotating in the same direction and acting as an external excitation on a specific surface of the plate. The stability analysis of the whole studied system (with two machines) around the obtained fixed point is done through analytical and numerical approaches by using the generalized Lyapunov and Routh-Hurwitz criterion. The existence conditions of the fixed point and the stability conditions are derived and presented. Great attention is put on the incidence of such study on the vibrations amplitude of the plate, which are considerably reduced in some cases. It appears that the time delay induces a rapid or late synchronization observed between the DC sources. This has been observed by numerically exploring the dynamics of the system for various possibilities that could occur. Moreover, in the modelling of the system, the positions on the plate occupied by DC electrical machines are taken into account by using the Heaviside function. It is shown that, in the case of three DC electrical machines, these positions influence the time to obtain a synchronous state between the DC electrical machines.

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Section: Stability Analysis Of the Systemmentioning

confidence: 99%

On Appearance of Fast or Late Self-Synchronization between Non-Ideal Sources Mounted on a Rectangular Plate Due to Time Delay

Djanan

Marburg

Nbendjo

2022

MCA

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“…The coupled in-phase synchronization in case of mechanical oscillators array is performed in [27]. Moreover, the chimera state of coupled pendulums, which is strictly connected with synchronization phenomenon is presented in [6,7]. Most of the scientific papers and all mentioned above, which give a big contribution to the knowledge of synchronization, focus on the pendulum dynamics in a vertical plane.…”

Section: Introductionmentioning

confidence: 99%

“…Fig 6. Beams displacement in the first resonance zone with frequency equal 5.9537 Hz-print screen from Abaqus software and time histories of individual beams ends and angle of hub rotation-symmetric model…”

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confidence: 99%

Vibration, synchronization and localization of three-bladed rotor: theoretical and experimental studies

Szmit

2021

Eur. Phys. J. Spec. Top.

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Numerical and experimental methods in free and forced vibrations of the rotating structure consisting of the rigid hub and three flexible beams are considered. Firstly, the system of four mutually coupled dimensionless differential governing equations is presented and then forced response of the system as well as synchronization phenomenon are investigated. Next, the finite elements method is used to design the rotating structure and analyse complex dynamic response. During the numerical calculations symmetric, as well as de-tuned rotor are analyzed. Finally, results obtained from ordinary differential equations and numerical simulations are compared with experimental tests.

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“…Complex synchronization transition and emergence phenomena occur when fractional-order neurons are coupled with memristive synapses, but there is no literature on this topic. The phenomenon of chimera states can describe the related degree of neurons in the network [33], and this phenomenon is widespread in neuronal networks [34][35][36][37][38], such as nonlocally and globally coupled time-delay Mackey-Glass oscillators [35], and subnetworks distributed in different regions of neuronal networks [38]. The chimera states, coherent states and incoherent states could be relevant for brain dynamics.…”

Section: Introductionmentioning

confidence: 99%

The Synchronization Behaviors of Memristive Synapse-Coupled Fractional-Order Neuronal Networks

Yang

Zhang

2021

IEEE Access

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The synchronization behaviors of memristive synapse-coupled fractional-order neuronal networks are investigated in this paper. Based on the integer-order memristive synapse-coupled neuronal network, a fractional-order model is proposed, and a ring network composed of fractional-order memristive synapse-coupled neuronal subnetworks is constructed. Then, the synchronization behaviors of two fractional-order memristive synapse-coupled neurons and the ring fractional-order memristive synapsecoupled neuronal network are discussed numerically. These research results suggest several novel phenomena and allow several conclusions to be drawn. For the two coupled neurons, different fractionalorders can change the threshold of memristive synapse parameter 1 k when the two neurons are in perfect synchronization. The synchronization transitions are affected by the fractional-order and memristive synapse. Different from the integer-order model, perfect synchronization can occur before phase synchronization for some fractional-orders. Under a certain external current intensity, the transition between periodic synchronization and chaotic synchronization occurs as the fractional-order changes. The chaotic synchronization range is larger because of the memristive synapse. For the ring neuronal network coupled subnetworks, the results illustrate that the collective behaviors including incoherent, coherent, and chimera states can be induced by the fractional-order. In addition, the network's synchronization degree is influenced by the fractional-order. The synchronization transition of the neuronal network also occurs with changes in the fractional-order.

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Traveling chimera states for coupled pendula

Cited by 34 publications

References 30 publications

On Appearance of Fast or Late Self-Synchronization between Non-Ideal Sources Mounted on a Rectangular Plate Due to Time Delay

On Appearance of Fast or Late Self-Synchronization between Non-Ideal Sources Mounted on a Rectangular Plate Due to Time Delay

Vibration, synchronization and localization of three-bladed rotor: theoretical and experimental studies

The Synchronization Behaviors of Memristive Synapse-Coupled Fractional-Order Neuronal Networks

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