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Arguments of differential weighting of steps cannot be brought to question these results, which are ultimately based on the syntenic relationships and patterns that have been used to support the WGD hypothesis in pairwise analyses [ 11, 12].
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This paper can be seen not only as the extension of asymptotically stable theory of differential equations with piecewise arguments in [14], but also as the extension of asymptotically stable theory of impulsive ordinary differential equations in [4].
The proofs are based on arguments of time-dependent variational inequalities, differential equations, and a fixed point theorem.
In the past three decades, the theory of differential equations with piecewise constant arguments has been intensively studied.
A nonlinear mathematical model of differential equations with piecewise constant arguments is proposed.
Later, the case of discontinuous solutions of differential equations with piecewise continuous arguments was proposed as an open problem by Wiener [9].
Later, oscillation of discontinuous solutions of differential equations with piecewise constant arguments has been proposed by Wiener as an open problem [2], p.380.
The theory of differential equation with piecewise constant arguments (EPCA) was initiated in [1, 2], which provided a mathematical instrument to applied science [3, 4].
The study of differential equations with piecewise constant argument (EPCA) initiated in [1, 2].
This idea can be used for the investigation of differential equations with piecewise constant argument of generalized type.
Therefore, the results of impulsive functional differential equations, especially for higher order impulsive functional differential equations, are fewer than those of differential equations without impulses and deviating arguments.
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