Coexistence of single- and multi-scroll chaotic orbits in a single-link flexible joint robot manipulator with stable spiral and index-4 spiral repellor types of equilibria

Singh, Jay Prakash; Lochan, Kshetrimayum; Kuznetsov, Nikolay V.; Roy, Binoy Krishna

doi:10.1007/s11071-017-3726-4

Cited by 47 publications

(10 citation statements)

References 68 publications

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“…NI Multisim components are based on actual circuit components. Simulation results obtained using NI Multisim are in consistence with the actual circuit results [26,30]. 6.…”

Section: Pitchfork Bifurcation In System (22)mentioning

confidence: 60%

“…For (m, r, g, k 1 , k 2 , k 3 , k 4 , k 5 , k 6 ) =(0.02, 0.02, 12, 0, 12, 0.001, 0.01, 0.01, −100), the circuit components in Fig. 10 are as follows: 2,7,8,15,16,22,23,26,28,29), R p = 1kΩ (p=4, 10,12,18,25,31,33) It is observed from Fig. 11 that the results obtained by circuit implementation of systems (2.2) confirm the MATLAB simulation results in Fig.…”

Section: Pitchfork Bifurcation In System (22)mentioning

confidence: 99%

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Coexisting hidden attractors in a 5D segmented disc dynamo with three types of equilibria

Bao¹,

Chen²,

Liu³

et al. 2019

Discrete &Amp; Continuous Dynamical Systems - B

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Little seems to be known about coexisting hidden attractors in hyperchaotic systems with three types of equilibria. Based on the segmented disc dynamo, this paper proposes a new 5D hyperchaotic system which possesses the properties. This new system can generate hidden hyperchaos and chaos when initial conditions vary, as well as self-excited chaotic and hyperchaotic attractors when parameters vary. Furthermore, the paper proves that the Hopf bifurcation and pitchfork bifurcation occur in the system. Numerical simulations demonstrate the emergence of the two bifurcations. The MATLAB simulation results are further confirmed and validated by circuit implementation using NI Multisim.

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“…NI Multisim components are based on actual circuit components. Simulation results obtained using NI Multisim are in consistence with the actual circuit results [26,30]. 6.…”

Section: Pitchfork Bifurcation In System (22)mentioning

confidence: 60%

Section: Pitchfork Bifurcation In System (22)mentioning

confidence: 99%

Coexisting hidden attractors in a 5D segmented disc dynamo with three types of equilibria

Bao¹,

Chen²,

Liu³

et al. 2019

Discrete &Amp; Continuous Dynamical Systems - B

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show abstract

“…erefore, when different initial conditions are taken, the coexisting and different attractors are exhibited. We know multistability is a critical property of nonlinear dynamical systems [41][42][43][44]. Since the crisis of the financial system is subject to various factors, the nature of the multi-steady state plays an important role in making correct decisions for government workers.…”

Section: Multistability In the Improved Financial System (3a)-(3c) Wimentioning

confidence: 99%

Hopf Bifurcation and Dynamic Analysis of an Improved Financial System with Two Delays

et al. 2020

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e complex chaotic dynamics and multistability of financial system are some important problems in micro-and macroeconomic fields. In this paper, we study the influence of two-delay feedback on the nonlinear dynamics behavior of financial system, considering the linear stability of equilibrium point under the condition of single delay and two delays. e system undergoes Hopf bifurcation near the equilibrium point. e stability and bifurcation directions of Hopf bifurcation are studied by using the normal form method and central manifold theory. e theoretical results are verified by numerical simulation. Furthermore, one feature of the proposed financial chaotic system is that its multistability depends extremely on the memristor initial condition and the system parameters. It is shown that the nonlinear dynamics of financial chaotic system can be significantly changed by changing the values of time delays.

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“…Excellent examples of potentially chaotic systems are mechanical oscillators. Early manuscripts were aimed on simple models describing Newtonian dynamics [14]- [17], object movement [18], etc. Unpredictable time evolutions were confirmed also in the case of simple mathematical models that describe biological populations [19], [20].…”

Section: Introductionmentioning

confidence: 99%

Minimal Realizations of Autonomous Chaotic Oscillators Based on Trans-Immittance Filters

Petržela

Polák

2019

IEEE Access

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This review paper describes a design process toward fully analog realizations of chaotic dynamics that can be considered canonical (minimum number of the circuit elements), robust (exhibit structurally stable strange attractors), and novel. Each autonomous chaotic lumped circuit proposed in this paper can be understood as a looped system, where linear trans-immittance frequency filter interacts with an active nonlinear two-port. The existence of chaos is demonstrated via well-established numerical algorithms that represent the current standard in the field of nonlinear dynamics, i.e., by calculation of the largest Lyapunov exponent and high-resolution 1-D bifurcation diagrams. The achieved numerical results are put into the context of experimental measurement; observed state trajectories prove a one-to-one correspondence between theoretical expectations and practical outputs, i.e., prescribed strange attractors do not represent the chaotic transients. Finally, short term unpredictability of the chaotic flow is demonstrated via calculation of Kaplan-Yorke dimension that is high, i.e., generated waveforms can find interesting applications in the fields of chaotic masking, modulation, or chaos-based cryptography.

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Coexistence of single- and multi-scroll chaotic orbits in a single-link flexible joint robot manipulator with stable spiral and index-4 spiral repellor types of equilibria

Cited by 47 publications

References 68 publications

Coexisting hidden attractors in a 5D segmented disc dynamo with three types of equilibria

Coexisting hidden attractors in a 5D segmented disc dynamo with three types of equilibria

Hopf Bifurcation and Dynamic Analysis of an Improved Financial System with Two Delays

Minimal Realizations of Autonomous Chaotic Oscillators Based on Trans-Immittance Filters

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