Almost periodic solutions

Date

2011-01-01

Author

Akhmet, Marat

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https://hdl.handle.net/11511/98925

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NONLINEAR HYBRID CONTINUOUS/DISCRETE-TIME MODELS

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Department of Mathematics, Article

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Almost periodic solutions of recurrently structured impulsive neural networks Top, Gülbahar; Akhmet, Marat; Department of Mathematics (2022-3-28) This thesis aims to conduct detailed and precise neural networks research with impulses at nonprescribed moments in terms of periodic and almost periodic solutions. Most of the actions in nature modeled by neural networks involve repetitions. Hence periodic and almost periodic motions become crucial. So in this thesis, the existence, uniqueness, and stability of the periodic and almost periodic motion are served for the neural networks with prescribed and nonprescribed impacts. This impulsive system is a n...
Almost Periodic Solutions of Recurrently Structured Impulsive Neural Networks Akhmet, Marat; Erim, Gülbahar (2022-01-01) ©2022 L&H Scientific Publishing, LLC. All rights reserved.The model under discussion is an elaborated recurrent impulsive neural network. This is the first time in literature that the impacts are structured completely as the original neural network, such that physical sense of impacts has been explained. Moreover, the impact part comprises all types of impacts in neural networks, which were traditionally studied in conservative models. In the research, neuron membranes with negative as well as positive capa...
Almost Periodic Solutions of Recurrent Neural Networks with State-Dependent and Structured Impulses Akhmet, Marat; Erim, Gülbahar (2023-01-01) The subject of the present paper is recurrent neural networks with variable impulsive moments. The impact activation functions are specified such that the structure for the jump equations are in full accordance with that one for the differential equation. The system studied in this paper covers the works done before, not only because the impacts have recurrent form, but also impulses are not state-dependent. The conditions for existence and uniqueness of asymptotically stable discontinuous almost periodic s...
Almost periodic solutions of differential equations with piecewise constant argument of generalized type Akhmet, Marat (Elsevier BV, 2008-06-01) We consider existence and stability of an almost periodic solution of the following hybrid system dx(t) dt = A(t)x(t) + f(t, x(θβ(t)−p1 ), x(θβ(t)−p2 ), . . . , x(θβ(t)−pm )), (1) where x ∈ R n , t ∈ R, β(t) = i if θi ≤ t < θi+1, i = . . .−2, −1, 0, 1, 2, . . . , is an identification function, θi is a strictly ordered sequence of real numbers, unbounded on the left and on the right, pj , j = 1, 2, . . . , m, are fixed integers, and the linear homogeneous system associated with (1) satisfies exponential dich...
Almost periodicity in chaos Akhmet, Marat (2018-01-01) Periodicity plays a significant role in the chaos theory from the beginning since the skeleton of chaos can consist of infinitely many unstable periodic motions. This is true for chaos in the sense of Devaney [1], Li-Yorke [2] and the one obtained through period-doubling cascade [3]. Countable number of periodic orbits exist in any neighborhood of a structurally stable Poincaré homoclinic orbit, which can be considered as a criterion for the presence of complex dynamics [4]-[6]. It was certified by Shilniko...

Citation Formats

M. Akhmet, “Almost periodic solutions,” NONLINEAR HYBRID CONTINUOUS/DISCRETE-TIME MODELS, vol. 8, pp. 105–119, 2011, Accessed: 00, 2022. [Online]. Available: https://hdl.handle.net/11511/98925.