2015
DOI: 10.1016/j.physleta.2015.06.039
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A chaotic system with a single unstable node

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Cited by 74 publications
(17 citation statements)
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“…Finally, after years of research dedicated to the autonomous dynamical systems, it seems that the existence of the multiple fixed points is not necessary for a vector field to exhibit chaotic behavior. Strange attractors can also be observed in dynamical systems with a single unstable node equilibrium, as previously demonstrated [19]. The most surprisingly unstable fixed points, which are normally responsible for strange attractor excitation and extreme sensitivity of dynamical system behavior to the initial conditions, can be changed into a single stable fixed point [20,21] or a pair of stable equilibria [22].…”
Section: Introductionsupporting
confidence: 53%
“…Finally, after years of research dedicated to the autonomous dynamical systems, it seems that the existence of the multiple fixed points is not necessary for a vector field to exhibit chaotic behavior. Strange attractors can also be observed in dynamical systems with a single unstable node equilibrium, as previously demonstrated [19]. The most surprisingly unstable fixed points, which are normally responsible for strange attractor excitation and extreme sensitivity of dynamical system behavior to the initial conditions, can be changed into a single stable fixed point [20,21] or a pair of stable equilibria [22].…”
Section: Introductionsupporting
confidence: 53%
“…Chaotic dynamical system having only one unstable node¯xed point is discussed in Ref. 32 and chaotic°ow with one nonhyperbolic¯xed point is a topic of Ref. 33.…”
Section: Introductionmentioning
confidence: 99%
“…Recently there has been an increasing effort in constructing new chaotic attractors with pre-designed types of equilibria [1][2][3][4][5][6][7][8][9][10][11][12]. These systems include dynamical systems with no equilibrium points [13][14][15][16][17][18][19][20][21], with only stable equilibria [22][23][24][25][26][27], with curves of equilibria [28][29][30], with surfaces of equilibria [8,9], and with non-hyperbolic equilibria [31,32].…”
Section: Introductionmentioning
confidence: 99%