Periodic solution of a prey–predator model with nonlinear state feedback control

Complex dynamics of an eco-epidemiological model with different competition coefficients and weak Allee in the predator

“…Mathematical model is a powerful tool for the investigation of the above mentioned behaviors, so different types of models have been developed and studied [44,60] . From mathematical point of view, as needs, we can classify them as deterministic models including models governed by ordinary differential equations [59,60] and by partial differential equations [44,75,86] and by fractional differential equations [91][92][93] and stochastic models [62] , models with time delays [96] , models with state feedback control [94] . Most of the deterministic predator-prey models explored local and global stability, persistence & community structure.…”

Periodic solution and control optimization of a prey-predator model with two types of harvesting

“…Recently, state-dependent impulse feedback control has attracted the attention of many scholars [19][20][21][22][23], a novel strategy based on state-dependent impulse feedback control is proposed and applied in the harvest [24][25][26][27] and pest management [28][29][30][31][32][33]. The procedure goes like this: when the number of species reaches a specific requirement, the harvesting strategy is implemented, otherwise the harvesting behavior is suppressed.…”

Dynamic analysis of unilateral diffusion Gompertz model with impulsive control strategy

“…With this in mind, the mathematical model of diffusion with pulse has been established, which makes the research more significant [6][7][8][9][10][11][12][13][14]. In particular, impulsive differential equations are very important in the research of population migration phenomenon [15][16][17][18][19][20][21][22][23][24]. Jiao et al [25] established a SIR model with pulse vaccination and proved the existence of a disease-free periodic solution, and a large pulse vaccination rate was a sufficient condition to eradicate the disease.…”