Extreme multistability in a Josephson-junction-based circuit

Louodop, Patrick; Tchitnga, Robert; Fagundes, Fernando F; Kountchou, Michaux; Tamba, V Kamdoun; Lambruschini, Carlos L. Pando; Cerdeira, Hilda A.

doi:10.1103/physreve.99.042208

Cited by 32 publications

(17 citation statements)

References 36 publications

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“…According to Sprott and Li, the importance of multistability resides in the fact that it is a common phenomenon in nature which, in practical engineering, can lead to unexpected and disastrous consequences [52]. Due to this importance, there is an intensive and active research on the topic [53,54,55].…”

Section: Bistability In the Resistorless Op-amp Based Oscillatormentioning

confidence: 99%

Non periodic oscillations, bistability, coexistence of chaos and hyperchaos in the simplest resistorless Op-Amp based Colpitts oscillator

Nanfa'a

Tchitnga

Louodop

et al. 2020

Heliyon

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In the framework of a project on simple circuits with unexpected high degrees of freedom, we report an autonomous microwave oscillator made of a CLC linear resonator of Colpitts type and a single general purpose operational amplifier (Op-Amp). The resonator is in a parallel coupling with the Op-Amp to build the necessary feedback loop of the oscillator. Unlike the general topology of Op-Amp-based oscillators found in the literature including almost always the presence of a negative resistance to justify the nonlinear oscillatory behavior of such circuits, our zero resistor circuit exhibits chaotic and hyperchaotic signals in GHz frequency domain, as well as many other features of complex dynamic systems, including bistability. This simplest form of Colpitts oscillator is adequate to be used as didactic model for the study of complex systems at undergraduate level. Analog and experimental results are proposed.

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Section: Bistability In the Resistorless Op-amp Based Oscillatormentioning

confidence: 99%

Non periodic oscillations, bistability, coexistence of chaos and hyperchaos in the simplest resistorless Op-Amp based Colpitts oscillator

Nanfa'a

Tchitnga

Louodop

et al. 2020

Heliyon

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“…The electrical circuit that we are analyzing is given by the following graph (See Figure 1) as presented in [62].…”

Section: Circuit and Model: Description Of Circuit Elementsmentioning

confidence: 99%

“…Summarizing, a single-component Josephson junction (JJ) (blue part of the circuit [63]- [68]) connected in parallel to a coil of inductance L, which is part of the C 1 -L-C 2 tank circuit series with a periodic force, while the Josephson junction, the nonlinear element, plays the feedback loop [62]. Applying Kirchhoff's law on the circuit on Figure 1, we obtain the following expressions:…”

Section: Circuit and Model: Description Of Circuit Elementsmentioning

confidence: 99%

Quantum Interferometry for Different Energy Landscapes in a Tuneable Josephson Junction Circuit

Nguenang¹,

Jipdi²,

Louodop³

et al. 2020

JAMP

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This paper presents a simple Josephson-junction circuit with two parameters (inductance and capacitance) which can be tuned to represent different energy landscapes with different physical properties. By tuning this quantum circuit through external accessible elements we can move from two to three and more energy levels depending on the parameter setting. The inductance, the capacitance as well as the external voltage (driving terms) condition the number of relevant energy levels as well as the model to be used.

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“…One of the most challenging dynamical phenomena, that is now widely investigated is the coexistence of more than one stable attractor in the phase space that is called multistability [22][23][24][25][26][27][28][29] . Typically, in multistable systems, we observe a few attractors, but there are from tens to infinite coexisting solutions in the furthest case that is called extreme multistability [30][31][32][33][34][35] . Usually analytical analysis of multistable systems requires simplifying equations or imposing strong assumptions on the solution.…”

Section: Introductionmentioning

confidence: 99%

An unified approach for the calculation of different sample-based measures with single sampling method

Leszczyński

Perlikowski

Brzeski

2023

Preprint

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This paper investigates two sample-based methods for analysing multistable systems, i.e., basin stability and basin entropy. Both methods are based on the large number of numerical integration trials obtained for a large set of different initial conditions. The obtained data is classified and used to determine measures that describe the stability of solutions, the structure of the phase space and the predictability of system dynamics. The basin stability reflects the overall probability of reaching given solutions, and the basin entropy measure was proposed to reflect the structure of basins of attraction and the complexity of their boundaries. While these two measures complement one another finely, the procedures originally proposed to obtain them differ significantly. The paper proposes a universal approach and algorithm to obtain the value of basin stability and basin entropy measures. The applicability of the proposed procedures is presented for two nonlinear systems.

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Extreme multistability in a Josephson-junction-based circuit

Cited by 32 publications

References 36 publications

Non periodic oscillations, bistability, coexistence of chaos and hyperchaos in the simplest resistorless Op-Amp based Colpitts oscillator

Non periodic oscillations, bistability, coexistence of chaos and hyperchaos in the simplest resistorless Op-Amp based Colpitts oscillator

Quantum Interferometry for Different Energy Landscapes in a Tuneable Josephson Junction Circuit

An unified approach for the calculation of different sample-based measures with single sampling method

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