Magnetic coupling based control of a chaotic circuit: Case of the van der Pol oscillator coupled to a linear circuit

Tegnitsap, Joakim Vianney Ngamsa; Fotsin, Hilaire Bertrand; Ngouonkadi, Elie Bertrand Megam

doi:10.1016/j.chaos.2021.111319

Cited by 11 publications

(7 citation statements)

References 30 publications

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“…This technology is used for example in daily life activities such as medical care, food quality detection, agriculture management systems services, and commerce [9][10][11][12][13][14]. 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: 85%

“…Each chaotic unit (Fig. 1(b)) is the VDPCL oscillator [80] which consists of two capacitors, one linear resistor, one nonlinear resistor, and two inductors. These inductors are magnetic core coils.…”

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

confidence: 99%

“…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%

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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: 85%

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

confidence: 99%

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

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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“…Note that several circuits modeling the van der Pol equation have been proposed both for low, medium and high-frequency applications. For low power, low frequency applications (50 Hz, 5 V), a circuit based on operational amplifier (AOP) and diode was proposed for SPICE simulation by Fotsin et al [41] and later confirmed experimentally by Ngamsa et al [42,43]. For low-power beam steering applications at micro-waves frequency, a model-based tunnel diode and transistor were used by A Semenov and O Semenova [44] and David Cordeau [1].…”

Section: Circuit Designmentioning

confidence: 99%

Dynamics of high-power coupled nonlinear oscillator arrays for electronic beam steering technique: case of the triode based van der Pol oscillator

Tsefack,

Tegnitsap,

Fotsin

et al. 2024

Phys. Scr.

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This paper presents the dynamics of coupled nonlinear oscillator arrays (CNOAs) as phase shifter for electronic beam steering technique. The proposed phase shifter uses oscillators of van der Pol type with a fifth-order nonlinear resistance and is built on the two architectures based injection-locked oscillator array (ILOAs) and coupled oscillator arrays (COAs). The dynamics equations of the phase shifter are proposed in the frequency and time domain. With the help of mathematical tools such as bifurcation diagrams, maximum Lyapunov exponent and Hilbert transform, important cartography of different oscillating states is deduced over large range of system parameters. Different behavior of the CNOAs including chaos, 2D-torus, multistability, locked and unlocked states are depicted. The phase shift between output voltages of each pair of coupled oscillators is presented for both architectures. A detailed analysis of locked states shows that the required phase shift is synthesized by slightly varying the frequency of the injected signal, or simply by detuning the free-running frequencies of the edge oscillators in equal but opposite directions. The proposed circuit of the phased shifter is built using the original van der Pol oscillator based on a vacuum triode. The maximal phase shift reaches 63° and 75° respectively for ILOAs and COAs. With the presence of triode in the circuit, the output voltage of each oscillating element in the array reaches 100 V around 60 KHz and is boosted by increasing the value of the triode bias potential to more than 420 V. This, therefore, increases the total power dissipation of a single oscillator in the array to more than 47 dB (50.12 W). This circuit is a candidate for high-power electronics beam steering at ultrasonic frequency.

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“…One of the problems in the synchronization of nonlinear oscillators is the synchronization of chaotic oscillators and sinusoidal oscillators [48][49][50][51]. Recently, the synchronization of the van der Pol oscillator coupled to a linear oscillator has been considered [52][53][54]. In [50], a sinusoidal oscillator is used to generate a chaotic signal.…”

Section: Introductionmentioning

confidence: 99%

Synchronization of Chaotic Memristive System with Sinusoidal Colpitts Oscillator based on Adaptive Feedback Control Method

Setoudeh,

Chegini

2023

Preprint

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The synchronization of chaotic memristive systems with sinusoidal oscillators in order to achieve fully sinusoidal response can be included among the most important ongoing research topics in nonlinear sciences. In this paper, the purpose of controlling the chaotic oscillator based on memristive devices is to achieve sinusoidal response by synchronizing its response with the response of sinusoidal colpitts oscillator. For this purpose, sinusoidal synchronizations between two distinct dynamical systems with different order are investigated. Accordingly, we provided a sufficient condition in order to control the chaos in the memristive oscillator based on memcapacitor and meminductor, in order to achieve fully sinusoidal response with constant amplitude. For this purpose, an adaptive feedback controller is designed to synchronize the states of the master and slave oscillators. Numerical simulations are performed to verify the effectiveness of the proposed control scheme.

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Magnetic coupling based control of a chaotic circuit: Case of the van der Pol oscillator coupled to a linear circuit

Cited by 11 publications

References 30 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

Dynamics of high-power coupled nonlinear oscillator arrays for electronic beam steering technique: case of the triode based van der Pol oscillator

Synchronization of Chaotic Memristive System with Sinusoidal Colpitts Oscillator based on Adaptive Feedback Control Method

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