Global stability of a novel nonlinear diffusion online game addiction model with unsustainable control

Kaihong Zhao; Kaihong Zhao

doi:10.3934/math.20221137

AIMS Mathematics

2022, Volume 7, Issue 12: 20752-20766. doi: 10.3934/math.20221137

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Research article

Global stability of a novel nonlinear diffusion online game addiction model with unsustainable control

Kaihong Zhao ^,

Department of Mathematics, School of Electronics & Information Engineering, Taizhou University, Zhejiang, Taizhou 318000, China

Received: 19 June 2022 Revised: 31 August 2022 Accepted: 12 September 2022 Published: 26 September 2022
MSC : 35K57, 35B40, 34K09, 92D25

In this paper, we build a novel nonlinear diffusion online game addiction model with unsustainable control. The existence and boundedness of a solution are investigated by a $ C_0 $-semigroup and differential inclusion. Simultaneously, we study the global asymptotic stability of steady states of the model. Finally, a concrete example is theoretically analyzed and numerically simulated.
- online game addiction model,
- reaction-diffusion,
- unsustainable control,
- global asymptotic stability
Citation: Kaihong Zhao. Global stability of a novel nonlinear diffusion online game addiction model with unsustainable control[J]. AIMS Mathematics, 2022, 7(12): 20752-20766. doi: 10.3934/math.20221137

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Abstract

In this paper, we build a novel nonlinear diffusion online game addiction model with unsustainable control. The existence and boundedness of a solution are investigated by a $ C_0 $-semigroup and differential inclusion. Simultaneously, we study the global asymptotic stability of steady states of the model. Finally, a concrete example is theoretically analyzed and numerically simulated.

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