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n-th-Order Simple Hyperjerk System with Unstable Equilibrium and Its Application as RPG

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Abstract

This paper presents a simple mathematical model with an electronic circuit for n-th-order hyperjerk system. For demonstration, the proposed iterative methodology comes with a fourth-order parametric control hyperjerk system that relies on the integrator, a summer amplifier, and an adjustable hyperbolic sine nonlinearity function. The proposed hyperjerk system exhibits exceptional unstable behavior at equilibrium. However, the corresponding hidden attractor near to equilibrium point has a high degree of disorder and randomness. The proposed n-th-order chaotic system has some important features such as simple model without multiplication term, simple circuitry, use of n number of capacitors, 2\((n-1)\) number of resistors, and sensitivity with passive components. Moreover, various dynamic behavior and typical time series chaotic responses of the proposed design are validated by incorporating bifurcation sequence, numerical simulation, and practical implementation by using Op-Amp. Also, an application perspective of the proposed hyperjerk system is extended to a random pulse generator (RPG). This concept reflects an idea to obtain the RPG by interfacing with the chaotic signals.

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Authors and Affiliations

  1. Department of Electronics and Communication Engineering, GL Bajaj Institute of Technology and Management, Greater Noida, Uttar Pradesh, India

    Manoj Joshi

  2. Department of Computer Science and Engineering, Indian Institute of Information Technology, Senapati, Manipur, India

    Prerna Mohit

  3. Department of Electronics and Communication Engineering, National Institute of Technology Manipur, Imphal, India

    Ashish Ranjan

Authors
  1. Manoj Joshi
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  2. Prerna Mohit
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  3. Ashish Ranjan
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Correspondence to Ashish Ranjan.

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Joshi, M., Mohit, P. & Ranjan, A. n-th-Order Simple Hyperjerk System with Unstable Equilibrium and Its Application as RPG. Circuits Syst Signal Process 40, 5913–5934 (2021). https://doi.org/10.1007/s00034-021-01752-3

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