Positive solutions and exponential stability of positive equilibrium of inertial neural networks with multiple time-varying delays
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This paper is concerned with positive solutions and global exponential stability of positive equilibrium of inertial neural networks with multiple time-varying delays. By utilizing the comparison principle via differential inequalities, we first explore conditions on damping coefficients and self-excitation coefficients to ensure that, with nonnegative connection weights and inputs, all state trajectories of the system initiating in an admissible set of initial conditions are always nonnegative. Then, based on the method of using homeomorphisms, we derive conditions in terms of linear programming problems via M-matrices for the existence, uniqueness, and global exponential stability of a positive equilibrium of the system. Two examples with numerical simulations are given to illustrate the effectiveness of the obtained results.
KeywordsInertial neural networks Positive equilibrium Exponential stability Time-varying delay
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The authors declare that no potential conflict of interest to be reported to this work.
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