@article{Liu2025, 
author = {Jie Liu and Bo Sang and Lihua Fan and Chun Wang and Xueqing Liu and Ning Wang and Irfan Ahmad},
title = {Symmetry, Hopf bifurcation, and offset boosting in a novel chameleon system},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {3},
pages = {4915-4937},
keywords = {Hopf bifurcation, antimonotonicity, bifurcation diagram, hidden chaotic attractor, offset boosting},
url = {https://www.sciopen.com/article/10.3934/math.2025225},
doi = {10.3934/math.2025225},
abstract = {Chameleon systems are dynamical systems that exhibit either self-excited or hidden oscillations depending on the parameter values. This paper presents a comprehensive investigation of a quadratic chameleon system, including an analysis of its symmetry, dissipation, local stability, Hopf bifurcation, and various chaotic dynamics as the control parameters    (  μ  ,  a  ,  c  ) vary. Here,    μ serves as the dissipation parameter in the    y direction. Bifurcation analysis for four scenarios with    μ  =  0 was performed, revealing the emergence of various dynamical phenomena under different parameter settings. Offset boosting means introducing a constant into one of the state variables of the system for boosting the variable to a different level. Additionally, hidden chaotic bistability with offset boosting was exhibited by varying    μ. The parameter    μ serves as both the Hopf bifurcation parameter and the offset boosting parameter, while the other parameters    (  a  ,  c  ) also play critical roles as control parameters, resulting in period-doubling routes to self-excited or hidden chaotic attractors. These findings enrich our understanding of nonlinear dynamics in quadratic chameleon systems.}
}