Circuit and microcontroller validation of the extreme multistable dynamics of a memristive Jerk system: application to image encryption

Njitacke, Zeric Tabekoueng; Feudjio, Cyrille; Signing, V. R. Folifack; Koumetio, Bernard Nzoko; Tsafack, Nestor; Awrejcewicz, Jan

doi:10.1140/epjp/s13360-022-02821-5

Cited by 14 publications

(5 citation statements)

References 75 publications

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“…The initial value of the system is chosen as a part of the key and the other part is chosen as two 8b random numbers p 1 and p 2 , the key K = { x 0 , y 0 , z 0 , ω 0 , p 1 , p 2 } . The above method is used to encrypt and analyze the ciphertext statistical properties, image correlation, key sensitivity, and information entropy [10].…”

Section: Image Encryptionmentioning

confidence: 99%

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A conservative system based on a triangular wave memristor and its application in image encryption

Liu

Zhang

et al. 2023

Preprint

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Reconstruction techniques can capture the attractor data of dissipative chaotic systems, which will lead to a threat to the security of the cryptosystem. Since conservative chaotic systems do not form chaotic attractors, they can avoid the defects of the dissipative system and resist attacks. This paper aims to construct a new type of active charge-controlled memristor based on a triangular wave and apply it to build a non-Hamiltonian globally conservative circuit, the characteristic roots of which are all on the imaginary axis. The system is critically stable and presents extremely high sensitivity to the initial values, exhibiting heterogeneous multistability and homogeneous multistability with local amplitude modulation. This special multistability is of great significance to engineering applications. In addition, as the hardware accuracy is limited and only a few conservative systems have been implemented digitally, the DSP platform is employed herein for the physical implementation of the proposed system. In the end, we applied the novel system to a plaintext-related image encryption algorithm. The results show that the system not merely can resist the risk of data reconstruction, but also has excellent random characteristics, and is suitable for encryption.

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Section: Image Encryptionmentioning

confidence: 99%

“…Since then, people found that the complex nonlinear properties of memristors can enhance the randomness and complexity of a chaotic system, and many of them are composed of memristors. Researchers have applied these systems to the field of encryption and achieved good results [10,11]. However, one major issue has concerned us.…”

Section: Introductionmentioning

confidence: 99%

A conservative system based on a triangular wave memristor and its application in image encryption

Liu

Zhang

et al. 2023

Preprint

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“…Rajagopal et al [14] proposed a new dissipative chaotic jerk system with two quadratic nonlinearities, discussed its dynamic properties, and provided a circuit realization of the new jerk system. Chaotic jerk systems have applications in many areas, such as oscillators [3,15], microcontrollers [16], circuits [17,18], memristors [19,20], encryption [21], etc.…”

Section: Introductionmentioning

confidence: 99%

“…We also demonstrate that the proposed mechanical jerk system can exhibit multistability with coexisting chaotic attractors. In fact, multistability is a special property of nonlinear dynamical systems, which refers to the coexistence of periodic orbits or chaotic attractors for the same set of system constants but considering different initial conditions or states [20,21].…”

Section: Introductionmentioning

confidence: 99%

FPGA-Based Implementation of a New 3-D Multistable Chaotic Jerk System with Two Unstable Balance Points

et al. 2023

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Mechanical jerk systems have applications in several areas, such as oscillators, microcontrollers, circuits, memristors, encryption, etc. This research manuscript reports a new 3-D chaotic jerk system with two unstable balance points. It is shown that the proposed mechanical jerk system exhibits multistability with coexisting chaotic attractors for the same set of system constants but for different initial states. A bifurcation analysis of the proposed mechanical jerk system is presented to highlight the special properties of the system with respect to the variation of system constants. A field-programmable gate array (FPGA) implementation of the proposed mechanical jerk system is given by synthesizing the discrete equations that are obtained by applying one-step numerical methods. The hardware resources are reduced by performing pipeline operations, and, finally, the paper concludes that the experimental results of the proposed mechanical jerk system using FPGA-based design show good agreement with the MATLAB simulations of the same system.

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“…In automotive engineering, controlling the jerk can help reduce the jarring effect of sudden acceleration or braking, improving ride comfort and safety [5,6]. As a nonlinear function, a jerk system can exhibit very complex and nonlinear behaviors, such as chaos or multistability [7,8]. The aim of studying the chaotic nonlinear dynamics of jerk systems is to understand the complex behavior that arises in systems that exhibit sudden changes in acceleration [9].…”

Section: Introductionmentioning

confidence: 99%

Energy function and complex dynamics from a jerk system

Yu,

Njitacke,

Jiang

et al. 2023

Phys. Scr.

Self Cite

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Jerk, as a mathematical concept, is used in mechanics to describe the rate of change of acceleration and plays a crucial role in the design of control systems for machines and vehicles. Therefore, it is important to master the various states and the energy released during the change of acceleration. This is why a new simple jerk function introduced afterward, energy released, is derived from a Hamilton function using the Helmholtz theorem. The condition of having a stable or unstable rate of change of acceleration is established using Hopf bifurcation theory. Some two-parameter stability charts are then computed for a suitable selection region of the study. Using some nonlinear analysis metrics, in the unstable region of the study, the occurrence of phenomena is found, such as reverse period doubling bifurcation, antimonotonicity, and hysteresis involving the coexistence of the states in the considered jerk system. An electronic circuit is built and used to implement the mathematical expression of the jerk equation and validate the result of the theoretical investigation.

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Circuit and microcontroller validation of the extreme multistable dynamics of a memristive Jerk system: application to image encryption

Cited by 14 publications

References 75 publications

A conservative system based on a triangular wave memristor and its application in image encryption

A conservative system based on a triangular wave memristor and its application in image encryption

FPGA-Based Implementation of a New 3-D Multistable Chaotic Jerk System with Two Unstable Balance Points

Energy function and complex dynamics from a jerk system

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