id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
cana-1090	Smitha Mary Mathew	Stability and Bifurcation in a Second-Order Difference System	2024	10	.pdf	application/pdf	3881	196	71	Its characteristic equation is given by 𝜆6 + 𝜆4(𝑎1𝑒−�̅� + 𝑎2𝑒−�̅� + 𝑎3𝑒−�̅�) + 𝜆3(𝑏2𝑐3𝑒−�̅�−�̅� + 𝑏1𝑐2𝑒−�̅�−�̅� + 𝑏3𝑐1𝑒−�̅�−�̅� + 𝑏1𝑏2𝑏3𝑒−�̅�−�̅�−�̅�) + 𝜆2(𝑎2𝑎3𝑒−�̅�−�̅� − 𝑏2𝑐3𝑧̅𝑒−�̅�−�̅� + 𝑎1𝑎3𝑒−�̅�−�̅� − 𝑏3𝑐1�̅�𝑒−�̅�−�̅� + 𝑎1𝑎2𝑒−�̅�𝑒−�̅� − 𝑏1𝑐2�̅�𝑒−�̅�𝑒−�̅� + 𝑒−�̅�−�̅�−�̅�[𝑏1𝑏2𝑏3�̅� + 𝑏1𝑏2𝑏3�̅� + 𝑏1𝑏2𝑏3𝑧̅]) + 𝜆𝑒−�̅�−�̅�−�̅�(−𝑏1𝑏2𝑏3�̅��̅� − 𝑏1𝑏2𝑏3�̅�𝑧̅ − 𝑏1𝑏2𝑏3�̅�𝑧̅ + 𝑎3𝑏1𝑐2 + 𝑎1𝑏2𝑐3 + 𝑎2𝑏3𝑐1) + 𝑒−�̅�−�̅�−�̅�(𝑎1𝑎2𝑎3 + 𝑏1𝑏2𝑏3�̅��̅�𝑧̅ + 𝑐1𝑐2𝑐3 − 𝑎2𝑏3𝑐1�̅� − 𝑎3𝑏1𝑐2�̅� − 𝑎1𝑏2𝑐3𝑧̅) = 0. |𝑎3𝑒−�̅�| + |𝑏1𝑏2𝑏3𝑒−�̅�−�̅�−�̅�| + |𝑏1𝑏2𝑏3�̅�𝑒−�̅�−�̅�−�̅�| + |𝑏1𝑏2𝑏3�̅�𝑒−�̅�−�̅�−�̅�| + |𝑏1𝑏2𝑏3𝑧̅𝑒−�̅�−�̅�−�̅�| + |𝑎1𝑎2𝑒−�̅�𝑒−�̅�| + |𝑎1𝑎3𝑒−�̅�𝑒−�̅�| + |𝑎2𝑎3𝑒−�̅�𝑒−�̅�| + |𝑏1𝑏2𝑏3�̅��̅�𝑒−�̅�−�̅�−�̅�| + |𝑏1𝑏2𝑏3�̅�𝑧̅𝑒−�̅�−�̅�−�̅�| + |𝑏1𝑏2𝑏3�̅�𝑧̅𝑒−�̅�−�̅�−�̅�| + |𝑎1𝑎2𝑎3𝑒−�̅�−�̅�−�̅�| + |𝑏1𝑏2𝑏3�̅��̅�𝑧̅𝑒−�̅�−�̅�−�̅�| < 1 Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 5s (2024) 558 https://internationalpubls.com is satisfied whenever 𝑎1𝑒−𝛼1[1 + 𝑎2𝑒−𝛼2] + 𝑎2𝑒−𝛼2[1 + 𝑎3𝑒−𝛼3] + 𝑎3𝑒−𝛼3[1 + 𝑎1𝑒−𝛼1] + 𝑎1𝑎2𝑎3𝑒−𝛼1𝑒−𝛼2𝑒−𝛼3 + 𝐵[�̅��̅�𝑧̅ + �̅��̅� + �̅�𝑧̅ + �̅�𝑧̅ + 𝑧̅ + �̅� + �̅� + 1] < 1. (31)	cache/cana-1090.pdf	txt/cana-1090.txt