Initial-Condition Effects on a Two-Memristor-Based Jerk System

Bao, Han; Ding, Ruoyu; Hua, Mengjie; Wu, Hsuan-Chung; Chen, Bei

doi:10.3390/math10030411

Cited by 17 publications

(15 citation statements)

References 40 publications

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“…In recent years, extreme multistability with the coexistence of infinitely many attractors [24][25][26][27][28] has attracted scientists' attention. This special phenomenon is frequently discovered in autonomous circuits and systems involving memory-circuit elements, since these circuits and systems have line or plane equilibrium sets [14,[29][30][31][32]. The stabilities of the equilibrium sets are determined by the initial conditions of memory-circuit elements, which induces the coexistence of infinitely many attractors.…”

Section: Introductionmentioning

confidence: 98%

Extreme Multistability and Its Incremental Integral Reconstruction in a Non-Autonomous Memcapacitive Oscillator

et al. 2022

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Extreme multistability has frequently been reported in autonomous circuits involving memory-circuit elements, since these circuits possess line/plane equilibrium sets. However, this special phenomenon has rarely been discovered in non-autonomous circuits. Luckily, extreme multistability is found in a simple non-autonomous memcapacitive oscillator in this paper. The oscillator only contains a memcapacitor, a linear resistor, a linear inductor, and a sinusoidal voltage source, which are connected in series. The memcapacitive system model is firstly built for further study. The equilibrium points of the memcapacitive system evolve between a no equilibrium point and a line equilibrium set with the change in time. This gives rise to the emergence of extreme multistability, but the forming mechanism is not clear. Thus, the incremental integral method is employed to reconstruct the memcapacitive system. In the newly reconstructed system, the number and stability of the equilibrium points have complex time-varying characteristics due to the presence of fold bifurcation. Furthermore, the forming mechanism of the extreme multistability is further explained. Note that the initial conditions of the original memcapacitive system are mapped onto the controlling parameters of the newly reconstructed system. This makes it possible to achieve precise control of the extreme multistability. Furthermore, an analog circuit is designed for the reconstructed system, and then PSIM circuit simulations are performed to verify the numerical results.

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Section: Introductionmentioning

confidence: 98%

Extreme Multistability and Its Incremental Integral Reconstruction in a Non-Autonomous Memcapacitive Oscillator

et al. 2022

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“…Many studies have been conducted on multifarious memristor-based application circuits and systems, involving the spiking and bursting neuron circuit [8], the multi-scroll memristive Hopfield neural network [9], and others, ever since physical accessibility of memristors was uncovered [10]. Given the inherent nonlinearity of memristor [11], memristors with peculiar nonlinear memductances were routinely introduced into some existing dynamical circuits or systems to construct various novel memristive dynamical circuits or systems, such as two-memristor-based Jerk system [12], no-equilibrium hyperchaotic multi-wing system [13], map-based neuron model [14], chaotic and hyper-chaotic systems [15], memristor-based hyperchaotic maps [16], memcapacitive oscillator [17], two-memristor-based hyper-jerk system [18], and others.…”

Section: Introductionmentioning

confidence: 99%

“…Memductance functions can often be split into two categories: smooth functions and non-smooth functions. Many memristor-based circuits and systems are explored using some conventional smooth functions, such as the hyperbolic tangent (Tanh) memductance function [12,19], quadric memductance function [20], sine memductance function [21], and others [22]. Absolute value memductance function is a common non-smooth function, and is often used to construct novel memristive system [23].…”

Section: Introductionmentioning

confidence: 99%

“…In actuality, extreme multistability mainly follows an unabridged smooth bifurcation route in regard to the initial conditions intuitively, and the bifurcation trajectories progressively changed [22]. The majority of recently published work, however, only concentrates on the extreme multistability connected to the memristor initial conditions (MIC) [22,31,32], and scarcely touches on the nonmemristor initial conditions (NMIC) [12]. To explore the intricate dynamics brought on by the memristors and non-memristors initial conditions, we present a novel memristive hyper-jerk system with a non-smooth ReLU memductance function in this article.…”

Section: Introductionmentioning

confidence: 99%

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Initial-condition effects on ReLU-type hyper-jerk system and its application in image encryption

Zhang,

Peng,

Chen

et al. 2023

Phys. Scr.

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Abstract：The memristive hyper-jerk system described in this study has a non-smooth Rectified Linear Unit (ReLU) memductance function. A non-smooth memductance function of this kind might cause the system to have three line equilibria within it, bring about the arrival of extreme multistability with infinitely many coexisting attractors. Analyzing the three line equilibria’s stabilities and researching the intricate dynamical effects triggered by memristor and non-memristor initial conditions are related topic. Phase portraits, bifurcation diagrams, Lyapunov exponent spectra, and the basins of attraction all show the dynamical tendencies. According to the results, the novel system’s dynamical behaviors depend on both the memristor initial condition and the non-memristor initial conditions. Moreover, PSIM circuit simulations and MCU-based hardware measurements are run to confirm the coexisting infinitely many attractors. The ReLU-type hyper-jerk system is then utilized to encrypt images. Experimental findings support its exceptional robustness against a range of potential attacks. 

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“…This feature translates into a high sensitivity to initial conditions [23] and also implies the impossibility of predicting the long-term evolution of chaotic systems. • Solutions of deterministic chaotic systems are generated by precise mathematical laws.…”

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confidence: 99%

Quality Evaluation for Reconstructing Chaotic Attractors

Frunzete

2022

Mathematics

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Dynamical systems are used in various applications, and their simulation is related with the type of mathematical operations used in their construction. The quality of the system is evaluated in terms of reconstructing the system, starting from its final point to the beginning (initial conditions). Deciphering a message has to be without loss, and this paper will serve to choose the proper dynamical system to be used in chaos-based cryptography. The characterization of the chaotic attractors is the most important information in order to obtain the desired behavior. Here, observability and singularity are the main notions to be used for introducing an original term: quality observability index (q.o.i.). This is an original contribution for measuring the quality of the chaotic attractors. In this paper, the q.o.i. is defined and computed in order to confirm its usability.

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Initial-Condition Effects on a Two-Memristor-Based Jerk System

Cited by 17 publications

References 40 publications

Extreme Multistability and Its Incremental Integral Reconstruction in a Non-Autonomous Memcapacitive Oscillator

Extreme Multistability and Its Incremental Integral Reconstruction in a Non-Autonomous Memcapacitive Oscillator

Initial-condition effects on ReLU-type hyper-jerk system and its application in image encryption

Quality Evaluation for Reconstructing Chaotic Attractors

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