Firstly, a novel six-dimensional (6D) hyperchaotic particle motion system is formulated. The equilibrium points and their characteristics, Poincaré sections, Lyapunov exponents, bifurcations and multi-periodic windows are studied. Secondly, we present two nonholonomic constrained systems. In order to analyze the particle motion trajectories under constraints, the explicit equations for constrained systems are given. Based on Lyapunov exponents, Poincaré maps and bifurcations, we can see that the different hyperchaotic phenomena of the particle motion can be generated by introducing nonholonomic constraints. Finally, the stability control of the 6D hyperchaotic particle motion system is realized by separately using constraint control method and linear feedback control method. Numerical simulations of the dynamical behaviors of the six-dimensional hyperchaotic particle motion system are carried out in order to illustrate the complex phenomena of the systems and verify the analysis results.
ChuZTengF.Short circuit current constrained UC in high IBG-Penetrated power systems. IEEE Trans Power Syst2021; 4: 760–775.
2.
LinSXuYWangJ.Coverage analysis and optimization for high-speed railway communication systems with narrow-strip-shaped cells. IEEE Trans Veh Technol2020; 69: 11544–11566.
3.
LiLWenGWangZ, et al. Efficient and secure image communication system based on compressed sensing for IoT monitoring applications. IEEE Trans Multimed2020; 22: 82–95.
4.
BizyaevIAMamaevIS.Separatrix splitting and nonintegrability in the nonholonomic rolling of a generalized Chaplygin sphere. Int J Nonlinear Mech2020; 126: 103550.
5.
AgúndezAGGarcía-VallejoDFreireE, et al. Stability analysis of a waveboard multibody model with toroidal wheels. Multibody Syst Dyn2021; 53: 1–31.
6.
FedonyukVTallapragadaP.The dynamics of a Chaplygin sleigh with an elastic internal rotor. Regul Chaot Dyn2019; 24: 114–126.
7.
DaluiSMajhiBRMishraP.Presence of horizon makes particle motion chaotic. Phys Lett B2018; 788: 486–493.
8.
GjataOZanolinF.An example of chaotic dynamics for the motion of a charged particle in a magnetic field. Nonlinear Anal2020; 201: 112091.
9.
BonfimOGriffithsDJHinkleyS.Chaotic and hyperchaotic motion of a charged particle in a magnetic dipole field. Int J Bifurcat Chaos2000; 10: 265–271.
10.
VaidyanathanSSambasAAbd-El-AttyB, et al. A 5-D multi-stable hyperchaotic two-disk dynamo system with no equilibrium point: circuit design, FPGA realization and applications to TRNGs and image encryption. IEEE Access2021; 9: 81352–81369.
11.
SuYWangX.Characteristic analysis of new four-dimensional autonomous power system and its application in color image encryption. Multimed Syst2022; 28(2): 553–571.
12.
SambasAVaidyanathanSZhangS, et al. Multistability analysis and multisim simulation of a 12-term double-scroll hyperchaos system with three nonlinear terms, bursting oscillations and its cryptographic applications. In: Abd El-LatifAAVolosC(eds.) Cybersecurity. Cham: Springer, 2022, pp.221–235.
13.
LiHHuaZBaoH, et al. Two-dimensional memristive hyperchaotic maps and application in secure communication. IEEE Trans Ind Electron2020; 68: 9931–9940.
14.
AlattasKAMostafaeeJSambasA, et al. Nonsingular integral-type dynamic finite-time synchronization for hyper-chaotic systems. Mathematics2022; 10: 2227–7390.
15.
BenkouiderKBoudenTSambasA, et al. A new 10-D hyperchaotic system with coexisting attractors and high fractal dimension: its dynamical analysis, synchronization and circuit design. PLoS One2022; 17: e0266053.
16.
SuarezOJLarozeDMartinez-MardonesJ, et al. Chaotic dynamics of a magnetic particle at finite temperature. Phys Rev B2017; 95: 014404.1–014404.9.
17.
HennigDBurbanksADOsbaldestinAH, et al. From collective periodic running states to completely chaotic synchronised states in coupled particle dynamics. Chaos2011; 21: 023132.
18.
ShiSGuJXuS, et al. Globally fixed-time high-order sliding mode control for new sliding mode systems subject to mismatched terms and its application. IEEE Trans Ind Electron2020; 67: 10776–10786.
19.
UtzTFleckCFrauhammerJ, et al. Extended Kalman filter and adaptive backstepping for mean temperature control of a three-way catalytic converter. Int J Robust Nonlinear Control2014; 24: 3437–3453.
20.
SetoguchiTMatsuoSShimamotoK, et al. Passive control of unsteady condensation shock wave. J Therm Sci2000; 9: 299–304.
21.
XieYZhaoTCaiG.Model reduction and active control for a flexible plate. Acta Mech Solida Sin2011; 24: 467–476.
22.
XuJLiuKLiuZ, et al. Electrothermal response optimization of nozzle structure for multi-material rapid prototyping based on fuzzy adaptive control. Rapid Prototyp J2022; 28: 1168–1181.
23.
PineDJGollubJPBradyJF, et al. Chaos and threshold for irreversibility in sheared suspensions. Nature2005; 438: 997–1000.
24.
LushiEVlahovskaPM.Periodic and chaotic orbits of plane-confined micro-rotors in creeping flows. J Nonlinear Sci2015; 25: 1111–1123.
25.
WigginsS.Global bifurcations and chaos: Analytical methods. New York, NY: Springer, 1988.
26.
WuXHuangTY.Computation of Lyapunov exponents in general relativity. Phys Lett A2003; 313: 77–81.
27.
YousufLS.Non-periodic motion reduction in globoidal cam with roller follower mechanism. Proc IMechE, Part C: J Mechanical Engineering Science2022; 236: 2714–2727.
28.
BandyDKBurtonEKTHallJR, et al. Predicting attractor characteristics using Lyapunov exponents in a laser with injected signal. Chaos2021; 31: 013120.
29.
WolfASwiftJBSwinneyHL, et al. Determining Lyapunov exponents from a time series. Phys D1985; 16: 285–317.
30.
RösslerOE.An equation for continuous chaos. Phys Lett A1976; 57: 397–398.
31.
HuangXZhaoZWangZ, et al. Chaos and hyperchaos in fractional-order cellular neural networks. Neurocomputing2012; 94: 13–21.
32.
ChangCMGeZM.Complete identification of chaos of nonlinear nonholonomic systems. Nonlinear Dyn2010; 60: 551–559.
33.
MeiFX.Fundamentals of nonholonomic system mechanics. Beijing: Beijing Institute of Technology Press, 1985.
34.
TaoYLiXRenJ.A repeated yielding model under periodic perturbation. Nonlinear Dyn2018; 94: 2511–2525.
35.
SahaATamangJWuGC, et al. Superperiodicity, chaos and coexisting orbits of ion-acoustic waves in a four-component nonextensive plasma. Commun Theor Phys2020; 72: 115501–116100.
36.
WangJLiuLLiuC.Sliding mode control with mismatched disturbance observer for chaotic oscillation in a seven-dimensional power system model. Int Trans Electr Energy Syst2020; 30: e12583.
37.
SajjadiSSBaleanuDJajarmiA, et al. A new adaptive synchronization and hyperchaos control of a biological snap oscillator. Fract2020; 138: 109919.
38.
WangFLiuC.A new criterion for chaos and hyperchaos synchronization using linear feedback control. Phys Lett A2006; 360: 274–278.
39.
EffatiSSaberi NikHJajarmiA.Hyperchaos control of the hyperchaotic Chen system by optimal control design. Nonlinear Dyn2013; 73: 499–508.
40.
MerkinDR.Introduction to the theory of stability. New York, NY: Springer, 1997.
41.
DeJesusEXKaufmanC.Routh-Hurwitz criterion in the examination of eigenvalues of a system of nonlinear ordinary differential equations. Phys Rev A1987; 35: 5288–5290.
42.
CaoJZhouSInmanDJ, et al. Chaos in the fractionally damped broadband piezoelectric energy generator. Nonlinear Dyn2015; 80: 1705–1719.
