id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-881	Zhang, Xiang; Kang, Ming; Geng, Fengjie	Dynamic behavior of a stochastic predator-prey model with stage-structure and nonlinear perturbation	2025	19	.pdf	application/pdf	8631	362	72	= − lnx1 − lnx2. 6 X. ZHANG, M. KANG, F. GENG EJDE-2025/32 Combining (3.1) and (3.2), we have LV1 = −r x2 x1 + αy +m+ d1 + (σ11 + σ12x1) 2 2 −m x1 x2 + sx2 + βy (1 + ax2)(1 + by) + d2 + (σ21 + σ22x2) 2 2 ≤ −rx2 x1 − mx1 x2 + αy +m+ d1 + σ2 11 2 + σ11σ12x1 + σ2 12 2 x2 1 + sx2 + β b + d2 + σ2 21 + σ2 22x 2 2 ≤ ( −2 √ rm+m+ d1 + β b + d2 + σ2 11 2 + σ2 21 ) + αy + σ11σ12x1 + σ2 12 2 x2 1 + sx2 + σ2 22x 2 2. (3.3) We define V2(x1) = u1(x1 + u2) v v , where u1 and u2 are positive constants which will be determined later, v ∈ (0, 1) is adequately small. +mx1( 1 √ x2 − 1 x2 )− σ2 12x 5 2 1 4 + σ2 12x 2 1 + pα 2 x2 1 − σ2 22x 5 2 2 4 + σ2 22x 2 2 + sx2 + qβ 2 x2 2 − σ2 32y 5 2 4 + αy + pα 2 y + qβ 2 y + δy + σ2 32y 2 +m 4 X. ZHANG, M. KANG, F. GENG EJDE-2025/32 + d1 + d2 + d3 + β b + σ2 11 + σ2 21 + σ2 31 ≤ rx2 4 + mx1 4 − σ2 12x 5 2 1 4 + σ2 12x 2 1 + pα 2 x2 1 − σ2 22x 5 2 2 4 + σ2 22x 2 2 + sx2 + qβ 2 x2 2 − σ2 32y 5 2 4 + αy + pα 2 y + qβ 2 y + δy + σ2 32y 2 +m+ d1 + d2 + d3 + β b + σ2 11 + σ2 21 + σ2 31 = ( −σ2 12x 5 2 1 4 + σ2 12x 2 1 + pα 2 x2 1 + mx1 4 )	cache/ejde-881.pdf	txt/ejde-881.txt