Cosmological Dynamics of a Hybrid Chameleon Scenario

Table 2

Eigenvalues and dynamical characters of the fixed points.

Point	Eigenvalues (𝜆1, 𝜆2, 𝜆3)	Stability
M	−32−32√𝜔−6𝛽𝜔𝑚−√6𝛽𝜔𝑛2+3𝑚^2−3𝑛^2,	Stable if 𝑚<(−2𝑛𝛽^2√𝑛^2+1+2√6𝛽√𝑛^2+1)√6(3𝑛+√6𝛽−3√𝑛^2+1)(−2𝑛𝛽+√6−2𝛽√𝑛^2+1)
	−3+3𝑚^2−3𝑛^2,−3+3𝑚^2−3𝑛^2	+(−3𝑛^2−3−2𝑛^2𝛽^2−2𝛽^2+3𝑛√𝑛^2+1)√6(3𝑛+√6𝛽−3√𝑛^2+1)(−2𝑛𝛽+√6−2𝛽√𝑛^2+1)
N	−3+3𝜔^2+2𝑚√6𝛽𝜔−2𝑛√6𝛽𝜔−1+𝜔,	Stable if 𝜔<1 and 𝑚<(3−3𝜔^2+2𝑛√6𝛽𝜔)√612𝛽𝜔
	−32+323𝜔,−2+32𝜔	Saddle point if 𝜔=0
P	−3+3𝜔^2+2𝑚√6𝛽𝜔−2𝑛√6𝛽𝜔−1+𝜔,	Stable if 𝜔<1 and 𝑚<3−3𝜔^2+2𝑛√6𝛽𝜔√612𝛽𝜔
	−32+323𝜔,−2+32𝜔	Saddle point if 𝜔=0
Q	(𝜆1𝑄, 𝜆2𝑄, 𝜆3𝑄)	Stable