Simple Chaotic Hyperjerk System

Dalkıran, Fatma Yıldırım; Sprott, Julien Clinton

doi:10.1142/s0218127416501893

Cited by 75 publications

(28 citation statements)

References 20 publications

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“…Recent studies [ 57 , 58 ] reveal the possibility to observe robust strange attractors within the dynamics of fourth-, fifth-, and even higher-order differential equations with many types and shapes of scalar nonlinearity, including quadratic polynomials. Such dynamical flows are usually coined in literature as hyperjerk systems.…”

Section: Numerical Analysis Of Chaotic Systems Dedicated For Circumentioning

confidence: 99%

New Nonlinear Active Element Dedicated to Modeling Chaotic Dynamics with Complex Polynomial Vector Fields

Petržela

Šotner

2019

Entropy

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This paper describes evolution of new active element that is able to significantly simplify the design process of lumped chaotic oscillator, especially if the concept of analog computer or state space description is adopted. The major advantage of the proposed active device lies in the incorporation of two fundamental mathematical operations into a single five-port voltage-input current-output element: namely, differentiation and multiplication. The developed active device is verified inside three different synthesis scenarios: circuitry realization of a third-order cyclically symmetrical vector field, hyperchaotic system based on the Lorenz equations and fourth- and fifth-order hyperjerk function. Mentioned cases represent complicated vector fields that cannot be implemented without the necessity of utilizing many active elements. The captured oscilloscope screenshots are compared with numerically integrated trajectories to demonstrate good agreement between theory and measurement.

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Section: Numerical Analysis Of Chaotic Systems Dedicated For Circumentioning

confidence: 99%

New Nonlinear Active Element Dedicated to Modeling Chaotic Dynamics with Complex Polynomial Vector Fields

Petržela

Šotner

2019

Entropy

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“…We can mention the Rossler system [2], Chen system [3], Jafari system [4], Pham system [5], and Lü system just to name a few [6]. In the last few years, special attention has been given to "jerk systems" because of their simplicity and complex dynamics [7][8][9][10][11][12]. From a mathematical point of view, a generalization of the jerk dynamics is usually given in the following form:…”

Section: Introductionmentioning

confidence: 99%

Coexistence of Multiple Points, Limit Cycles, and Strange Attractors in a Simple Autonomous Hyperjerk Circuit with Hyperbolic Sine Function

et al. 2020

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In this contribution, a new elegant hyperjerk system with three equilibria and hyperbolic sine nonlinearity is investigated. In contrast to other models of hyperjerk systems where either hidden or self-excited attractors are obtained, the case reported in this work represents a unique one which displays the coexistence of self-excited chaotic attractors and stable fixed points. The dynamic properties of the new system are explored in terms of equilibrium point analyses, symmetry and dissipation, and existence of attractors as well. Common analysis tools (i.e., bifurcation diagram, Lyapunov exponents, and phase portraits) are used to highlight some important phenomena such as period-doubling bifurcation, chaos, periodic windows, and symmetric restoring crises. More interestingly, the system under consideration shows the coexistence of several types of stable states, including the coexistence of two, three, four, six, eight, and ten coexisting attractors. In addition, the system is shown to display antimonotonicity and offset boosting. Laboratory experimental measurements show a very good coherence with the theoretical predictions.

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“…What’s more, Recai Kilic introduced a universal approach to design and implement programmable analog non-time-delay chaotic systems based on FPAA [ 13 ]. After that, Fatma Yildirim Dalkiran and J. C. Sprott realized a fourth-order hyperjerk system based on FPAA [ 14 ]. Chunbiao Li designed and implemented chaotic systems with complete amplitude control and constructed infinitely many attractors in a programmable chaotic circuit based on FPAA [ 15 , 16 ].…”

Section: Introductionmentioning

confidence: 99%

Design and Implementation of Autonomous and Non-Autonomous Time-Delay Chaotic System Based on Field Programmable Analog Array

Liu

Xie

2019

Entropy

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Time-delay chaotic systems can have hyperchaotic attractors with large numbers of positive Lyapunov exponents, and can generate highly stochastic and unpredictable time series with simple structures, which is very suitable as a secured chaotic source in chaotic secure communications. But time-delay chaotic systems are generally designed and implemented by using analog circuit design techniques. Analog implementations require a variety of electronic components and can be difficult and time consuming. At this stage, we can now solve this question by using FPAA (Field-Programmable Analog Array). FPAA is a programmable device for implementing multiple analog functions via dynamic reconfiguration. In this paper, we will introduce two FPAA-based design examples: An autonomous Ikeda system and a non-autonomous Duffing system, to show how a FPAA device is used to design programmable analog time-delay chaotic systems and analyze Shannon entropy and Lyapunov exponents of time series output by circuit and simulation systems.

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Simple Chaotic Hyperjerk System

Cited by 75 publications

References 20 publications

New Nonlinear Active Element Dedicated to Modeling Chaotic Dynamics with Complex Polynomial Vector Fields

New Nonlinear Active Element Dedicated to Modeling Chaotic Dynamics with Complex Polynomial Vector Fields

Coexistence of Multiple Points, Limit Cycles, and Strange Attractors in a Simple Autonomous Hyperjerk Circuit with Hyperbolic Sine Function

Design and Implementation of Autonomous and Non-Autonomous Time-Delay Chaotic System Based on Field Programmable Analog Array

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