Results 11 to 20 of about 10,716 (259)
Chaotic Dynamics by Some Quadratic Jerk Systems [PDF]
Axioms, 2021 This paper is about the dynamical evolution of a family of chaotic jerk systems, which have different attractors for varying values of parameter a. By using Hopf bifurcation analysis, bifurcation diagrams, Lyapunov exponents, and cross sections, both self-excited and hidden attractors are explored.
Mei Liu +3 more
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Zero-Hopf bifurcation in a 3D jerk system [PDF]
Nonlinear Analysis: Real World Applications, 2021 We consider the 3-D system defined by the jerk equation $\dddot{x} = -a \ddot{x} + x \dot{x}^2 -x^3 -b x + c \dot{x}$, with $a, b, c\in \mathbb{R}$. When $a=b=0$ and $c < 0$ the equilibrium point localized at the origin is a zero-Hopf equilibrium. We analyse the zero-Hopf Bifurcation that occur at this point when we persuade a quadratic perturbation
Francisco Braun, Ana C. Mereu
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Mathematics, 2023 This research paper addresses the modelling of a new 3-D chaotic jerk system with a stable equilibrium. Such chaotic systems are known to exhibit hidden attractors.
Sundarapandian Vaidyanathan +7 more
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IEEE Access, 2023 In this paper, we propose a novel 3-D jerk system with three quadratic nonlinear terms and demonstrate the dynamical properties of the proposed jerk system in terms of phase portraits, bifurcation diagrams, Lyapunov exponents, multistability and ...
Talal Bonny +5 more
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Applied Sciences, 2021 In this work, we propose a convenient method for evaluating levels of angular jerk in augmented reality (AR) and virtual reality (VR). Jerk is a rarely analyzed metric in usability studies, although it can be measured and calculated easily with most head-
Jared Van Dam +3 more
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Jerk forms dynamics of a Chua’s family and their new unified circuit implementation
IET Circuits, Devices and Systems, 2021 A scheme to implement the Jerk form of the Chua system family using a controllable canonical form applied in linear systems is proposed. The main thought is that the nonlinear function with a single independent variable input can be superposed by a ...
Wei Xu, Ning Cao
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Chaos Theory and Applications, 2021 An effective design procedure has been introduced for implementing the fractional order integrator structures with a modified low pass filters (LPFs) and its functionality is verified by realizing a fractional-order chaotic system. In these applications,
Nimet Korkmaz, İbrahim Ethem Saçu
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On Hopf and Fold Bifurcations of Jerk Systems
Mathematics, 2023 In this paper we consider a jerk system x˙=y,y˙=z,z˙=j(x,y,z,α), where j is an arbitrary smooth function and α is a real parameter. Using the derivatives of j at an equilibrium point, we discuss the stability of that point, and we point out some local codim-1 bifurcations.
Cristian Lăzureanu, Jinyoung Cho
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The chaotic mechanisms in some jerk systems
AIMS Mathematics, 2022 <abstract><p>In this work, a five-parameter jerk system with one hyperbolic sine nonlinearity is proposed, in which $ \varepsilon $ is a small parameter, and $ a $, $ b $, $ c $, $ d $ are some other parameters. For $ \varepsilon = 0 $, the system is $ Z_{2} $ symmetric. For $ \varepsilon \neq {0} $, the system loses the symmetry.
Xiaoyan Hu, Bo Sang, Ning Wang
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A novel 3-D jerk chaotic system with three quadratic nonlinearities and its adaptive control
Archives of Control Sciences, 2016 This paper announces an eight-term novel 3-D jerk chaotic system with three quadratic nonlinearities. The phase portraits of the novel jerk chaotic system are displayed and the qualitative properties of the jerk system are described.
Vaidyanathan Sundarapandian
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