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Some new insights into a known Chen‐like system
Author(s) -
Wang Haijun,
Li Xianyi
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3599
Subject(s) - mathematics , pitchfork bifurcation , heteroclinic bifurcation , biological applications of bifurcation theory , heteroclinic cycle , bifurcation , degenerate energy levels , lyapunov exponent , bogdanov–takens bifurcation , heteroclinic orbit , equilibrium point , hopf bifurcation , nonlinear system , chaotic , bifurcation theory , saddle node bifurcation , mathematical analysis , homoclinic orbit , differential equation , physics , computer science , quantum mechanics , artificial intelligence
In the paper entitled ‘A novel chaotic system and its topological horseshoe’ in [Nonlinear Analysis: Modelling and Control 18 (1) (2013) 66–77], proposed the 3D chaotic system,x ̇ = a ( y − x ) + yz , y ̇ = ( c − a ) x − xz + cy , ż = e y 2 − bz , and discussed some of its dynamics according to theoretical and numerical analysis of its parameters ( a , b , c , e ) ∈ R+ 4. The present work is devoted to giving some new insights into the system for b ≥0. Combining theoretical analysis and numerical simulations, some new results are formulated. On the one hand, after some known errors, mainly the distribution of its equilibrium point which is pointed out, correct results are formulated. On the other hand, some of its more rich dynamical properties hiding and not found previously, such as the stability, fold bifurcation, pitchfork bifurcation, degenerated pitchfork bifurcation, and Hopf bifurcation of its isolated equilibria, the dynamics of non‐isolated equilibria, the singularly degenerate heteroclinic cycle, the heteroclinic orbit, and the dynamics at infinity are clearly revealed. Using these results, one can easily explain those interesting phenomena for invariant Lyapunov exponent spectrum and amplitude control that are presented in the known literature. What is more important, we probably demonstrate a new route to chaos. Copyright © 2015 John Wiley & Sons, Ltd.