Multistability, transient chaos and hyperchaos, synchronization, and chimera states in wireless magnetically coupled VDPCL oscillators

Tegnitsap, Joakim Vianney Ngamsa; Fotsin, Hilaire Bertrand

doi:10.1016/j.chaos.2022.112056

Cited by 6 publications

(4 citation statements)

References 33 publications

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“…Also, in our recent papers, we show that chaotic-based inductor oscillators can be wirelessly controlled when coupled magnetically to another external coil supplied by a sinusoidal voltage [15]. Other recent papers have also shown that magnetic coupling can be used to generate very rich dynamics in unconnected coupled chaotic oscillators including synchronization and chimera state [16,17].…”

Section: Introductionmentioning

confidence: 65%

“…are respectively the coupling coefficient between inductors 𝐿 1 and 𝐿 2 . Since the model is based on unconnected circuits, these coupling coefficients depend on the distance between each oscillator and the geometry of the coils [15][16][17]. Also, the current-voltage characteristic of the nonlinear resistor is given by 𝑖(𝑉 1 ) = 𝑎𝑉 1 + 𝑏𝑉 1 3 with 𝑎 < 0 and 𝑏 > 0.…”

Section: Network Configuration and Mathematical Model 21 Network Conf...mentioning

confidence: 99%

“…Chimera state has been first observed in non-local coupling [33][34][35][36][37] and it was believed that a nonlocal coupling topology is the necessary condition for the appearance of chimera states in complex networks. However, recent studies have demonstrated the emergence of chimera states in a variety of topologies including global [38][39][40][41][42][43]17] and local (nearest-neighbor) [44,45,31] coupled oscillators, and, for different types of individual dynamics such as limit-cycle oscillators [45,46] chaotic oscillators [47], chaotic maps [48], hyperchaotic time delay systems [49], and even in neuronal systems exhibiting bursting dynamics [50][51][52]. A pioneering work that unveils this dynamical pattern is the work of Bathogoh and Kuramuto [53].…”

Section: Introductionmentioning

confidence: 99%

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Complex spatiotemporal dynamics in a network of locally and magnetically coupled VDPCL oscillators

Tegnitsap

Kengne

Nkengfack

et al. 2023

Preprint

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Nowadays, we are witnessing a dramatic advance in wireless technology-based magnetic induction. It is used both for wireless power transfer and data transfer between systems. In addition, it is widely shown that a network of coupled identical oscillators exhibits complex collective behavior characterized by the coexistence of coherent and incoherent domains and termed as chimera state. In this paper, we consider a network of (N ≥10) locally and magnetically coupled Van der Pol oscillators coupled to a linear circuit (VDPCL oscillators). We then investigate the different arrangements of their interactions in terms of the magnetic coupling coefficients, taken as the bifurcation parameters. Statistical measure namely the strength of incoherence is used to classify the synchronized states in the network. Another algorithm described in the text is used for the classification and is consistent with the strength of incoherence. Numerical simulation reveals that the emerging spatiotemporal behaviors depend on the choice of initial conditions revealing the presence of multistability in the network. This network configuration also reveals a rich repertoire of spatiotemporal dynamics such as coherence/global synchronization, decoherence, chimera state, cluster synchronization, and solitary states as the magnetic coupling coefficients vary. Some other interesting behaviors such as traveling clustered wave, double and multicluster chimera state, and clustered solitary state for a specific set of initial conditions are also obtained. Furthermore, Pspice-based simulations carried out for a network of (N=10) oscillators are consistent with the numerical simulations based on the mathematical model.

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Section: Introductionmentioning

confidence: 65%

Section: Network Configuration and Mathematical Model 21 Network Conf...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Complex spatiotemporal dynamics in a network of locally and magnetically coupled VDPCL oscillators

Tegnitsap

Kengne

Nkengfack

et al. 2023

Preprint

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show abstract

“…Because it can be applied in multiple fields, studying the transient behavior of a chaotic system is more instructive for practical applications. [34] However, most chaotic systems have very few transient behaviors, typically only periodic to chaotic transitions, [35,36] or transitions from chaos to periodicity. [37] Although a memristive chaotic system with four transient behaviors has recently been reported, [34] and scholars have discovered systems with two transient behaviors coexisting, [38] as well as some other special transient behaviors, [39][40][41] such systems are still rare.…”

Section: Introductionmentioning

confidence: 99%

Rucklidge-based memristive chaotic system: Dynamic analysis and image encryption

et al. 2023

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A new four dimensional memristive chaotic system is obtained by introducing a memristor into the Rucklidge chaotic system, and a detailed dynamic analysis of the system is performed. The sensitivity of the system to parameters allows it obtains 16 different attractors by changing only one parameter. The various transient behaviors and excellent spectral entropy and C0 complexity values of the system can also reflect the high complexity of the system. A circuit is designed and verified the feasibility of the system from the physical level. Finally, the system is applied to image encryption, and the security of the encryption system is analyzed from multiple aspects, providing a reference for the application of such memristive chaotic systems.

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Transient dynamics in a quasiperiodically forced nonsmooth dynamical system

Li,

Duan,

et al. 2024

Nonlinear Dyn

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Multistability, transient chaos and hyperchaos, synchronization, and chimera states in wireless magnetically coupled VDPCL oscillators

Cited by 6 publications

References 33 publications

Complex spatiotemporal dynamics in a network of locally and magnetically coupled VDPCL oscillators

Complex spatiotemporal dynamics in a network of locally and magnetically coupled VDPCL oscillators

Rucklidge-based memristive chaotic system: Dynamic analysis and image encryption

Transient dynamics in a quasiperiodically forced nonsmooth dynamical system

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