Diagnosing multistability by offset boosting

An offset-boosting-based approach is developed for multistability identification in dynamical systems, where nonbifurcation operations are used for diagnosing multistability. Compared with the amplitude control method, the proposed approach has three distinguished features: easiness to introduce a parameter for offset boosting; reliability for finding coexisting attractors from arbitrary initial conditions; vigilance for identifying coexisting symmetric pairs of attractors. The proposed approach can identify coexisting hidden or self-excited attractors.

[1]  Julien Clinton Sprott,et al.  Crisis in Amplitude Control Hides in Multistability , 2016, Int. J. Bifurc. Chaos.

[2]  F. Arecchi,et al.  Experimental evidence of subharmonic bifurcations, multistability, and turbulence in a Q-switched gas laser , 1982 .

[3]  Chunhua Yuan,et al.  Adaptive complex modified projective synchronization of complex chaotic (hyperchaotic) systems with uncertain complex parameters , 2015 .

[4]  Ertugrul M. Ozbudak,et al.  Multistability in the lactose utilization network of Escherichia coli , 2004, Nature.

[5]  Julien Clinton Sprott,et al.  Hypogenetic chaotic jerk flows , 2016 .

[6]  Buncha Munmuangsaen,et al.  A new five-term simple chaotic attractor , 2009 .

[7]  Julien Clinton Sprott,et al.  Multistability in the Lorenz System: A Broken Butterfly , 2014, Int. J. Bifurc. Chaos.

[8]  Anda Xiong,et al.  Classifying and quantifying basins of attraction. , 2015, Chaos.

[9]  Foss,et al.  Multistability and delayed recurrent loops. , 1996, Physical review letters.

[10]  Bocheng Bao,et al.  Multistability induced by two symmetric stable node-foci in modified canonical Chua’s circuit , 2017 .

[11]  Julien Clinton Sprott,et al.  Variable-boostable chaotic flows , 2016 .

[12]  Julien Clinton Sprott,et al.  Recent new examples of hidden attractors , 2015 .

[13]  Bocheng Bao,et al.  Hidden extreme multistability in memristive hyperchaotic system , 2017 .

[14]  Tomasz Kapitaniak,et al.  Multistability: Uncovering hidden attractors , 2015, The European Physical Journal Special Topics.

[15]  Julien Clinton Sprott,et al.  Adaptive complex modified hybrid function projective synchronization of different dimensional complex chaos with uncertain complex parameters , 2016 .

[16]  M Laurent,et al.  Multistability: a major means of differentiation and evolution in biological systems. , 1999, Trends in biochemical sciences.

[17]  Julien Clinton Sprott,et al.  Constructing chaotic systems with conditional symmetry , 2017 .

[18]  Min Xiao,et al.  Optical multistability in three-level atoms inside an optical ring cavity. , 2003, Physical review letters.

[19]  Julien Clinton Sprott,et al.  Multistability in symmetric chaotic systems , 2015 .

[20]  Julien Clinton Sprott,et al.  Simplest Chaotic Flows with Involutional Symmetries , 2014, Int. J. Bifurc. Chaos.

[21]  Julien Clinton Sprott,et al.  Coexisting Hidden Attractors in a 4-D Simplified Lorenz System , 2014, Int. J. Bifurc. Chaos.

[22]  Bocheng Bao,et al.  Multiple attractors in a non-ideal active voltage-controlled memristor based Chua's circuit , 2016 .

[23]  G. Leonov,et al.  Localization of hidden Chuaʼs attractors , 2011 .

[24]  Qiang Lai,et al.  Generating Multiple Chaotic Attractors from Sprott B System , 2016, Int. J. Bifurc. Chaos.

[25]  Julien Clinton Sprott,et al.  Amplitude control approach for chaotic signals , 2013 .

[26]  Julien Clinton Sprott,et al.  Finding coexisting attractors using amplitude control , 2014 .

[27]  Rongrong Wang,et al.  A new finding of the existence of hidden hyperchaotic attractors with no equilibria , 2014, Math. Comput. Simul..

[28]  Julien Clinton Sprott,et al.  Constructing Chaotic Systems with Total Amplitude Control , 2015, Int. J. Bifurc. Chaos.

[29]  Qiang Lai,et al.  Research on a new 3D autonomous chaotic system with coexisting attractors , 2016 .

[30]  G. Leonov,et al.  Hidden attractors in dynamical systems , 2016 .

[31]  Julien Clinton Sprott,et al.  Multistability in a Butterfly Flow , 2013, Int. J. Bifurc. Chaos.

[32]  Julien Clinton Sprott,et al.  A dynamical system with a strange attractor and invariant tori , 2014 .

[33]  Zhouchao Wei,et al.  Hidden chaotic attractors in a class of two-dimensional maps , 2016 .

[34]  Leo R. M. Maas,et al.  The diffusionless Lorenz equations; Shil'nikov bifurcations and reduction to an explicit map , 2000 .

[35]  Jacques Kengne,et al.  Coexistence of Multiple Attractors and Crisis Route to Chaos in a Novel Chaotic Jerk Circuit , 2016, Int. J. Bifurc. Chaos.

[36]  B. Bao,et al.  Multistability in Chua's circuit with two stable node-foci. , 2016, Chaos.

[37]  Jacques Kengne,et al.  Dynamical analysis of a simple autonomous jerk system with multiple attractors , 2016 .

[38]  Julien Clinton Sprott,et al.  Coexistence of Point, periodic and Strange attractors , 2013, Int. J. Bifurc. Chaos.