On the reduction principle for differential equations with piecewise constant argument of generalized type

Abstract

In this paper we introduce a new type of differential equations with piecewise constant argument (EPCAG), more general than EPCA [K.L. Cooke, J. Wiener, Retarded differential equations with piecewise constant delays, (in Russian)] is proved for EPCAG. The structure of the set of solutions is specified. We establish also the existence of global integral manifolds of quasilinear EPCAG in the so-called critical case and investigate the stability of the zero solution.

Stability in cellular neural networks with a piecewise constant argument

“…Particularly, one cannot investigate the problem of stability completely, as only elements of a countable set are allowed to be discussed for initial moments. By introducing arbitrary piecewise constant functions as arguments, the concept of differential equations with a piecewise constant argument has been generalized in [1][2][3][4], where an integral representation formula was proposed as another approach to meet the challenges discussed above.…”

Variational Iteration Method for Solving Differential Equations with Piecewise Constant Arguments

“…In order to overcome the difficulty from the greatest integer function []  , we can consider the above iteration formula in a series of intervals: [0, 2) , [2,4) , [4,6) , …, [2 , 2( 1)) nn  where 0,1, 2, n  …. Following this way, each integral in iteration formulas will be easily computed.…”

“…Recently, there has been much research concerning properties of solutions of differential equations with piecewise constant arguments (EPCA) [1][2][3][4]. In these equations, the derivatives of the unknown functions depend on not just the time t before t .…”

Stabilization control of generalized type neural networks with piecewise constant argument

“…Due to its potential applications in various fields, generalized type system with piecewise constant argument has been widely investigated in recent years ( [1][2][3][4][5][6][7]). Different from that the traditional system can only be delayed or advanced, generalized type system can change its type of deviation of the parameters during the motion, and hence can be both delayed and advanced.…”