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Unpredictable and Poisson Stable Oscillations of Inertial Neural Networks with Generalized Piecewise Constant Argument [PDF]
Entropy, 2023 A new model of inertial neural networks with a generalized piecewise constant argument as well as unpredictable inputs is proposed. The model is inspired by unpredictable perturbations, which allow to study the distribution of chaotic signals in neural ...
Marat Akhmet +2 more
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Periodic Solutions for Nonlinear Integro-Differential Systems with Piecewise Constant Argument [PDF]
The Scientific World Journal, 2014 We investigate the existence of the periodic solutions of a nonlinear integro-differential system with piecewise alternately advanced and retarded argument of generalized type, in short DEPCAG; that is, the argument is a general step function.
Kuo-Shou Chiu
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Periodic Solutions of Certain Differential Equations with Piecewise Constant Argument [PDF]
International Journal of Mathematics and Mathematical Sciences, 2015 Existence criteria are derived for the eventually periodic solutions of a class of differential equations with piecewise constant argument whose solutions at consecutive integers satisfy nonlinear recurrence relations. The proof characterizes the initial
James Guyker
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Oscillatory and Nonoscillatory Delay Equations with Piecewise Constant Argument
Journal of Mathematical Analysis and Applications, 2000 The authors consider the linear delay differential equation with piecewise constant deviating argument of the form \[ y'(t)+ a(t)y(t)+b(t)y([t-1])=0,\quad t\geq 0, \tag{1} \] where \(a(t),\;b(t)\) are continuous functions on \([-1,\infty),\;b(t)\geq 0(\not\equiv 0)\) for \(t\geq 0\), and \([\cdot ]\) denotes the greatest integer function.
I P Stavroulakis
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Lyapunov-Razumikhin method for differential equations with piecewise constant argument
Discrete and Continuous Dynamical Systems, 2009 At the first time, Razumikhin technique is applied for differential equations with piecewise constant argument of generalized type [1, 2]. Sufficient conditions are established for stability, uniform stability and uniform asymptotic stability of the trivial solution of such equations. We also provide appropriate examples to illustrate our results.
Marat Akhmet
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Asymptotic behaviour of a population model with piecewise constant argument
Applied Mathematics Letters, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On Quasi-Periodic Solutions of Differential Equations with Piecewise Constant Argument
Journal of Mathematical Analysis and Applications, 2002 It is shown that \[ x'(t)= ax(t)+ \sum^N_{j=-N} a_j x([t+ j])+ f(t)\tag{\(*\)} \] has a unique quasiperiodic (qp) solution \(x\in QP(\omega_1,\dots, \omega_r)\) whenever \(f\in QP(\omega_1,\dots, \omega_r):= \{g:\mathbb{R}\to \mathbb{R}: g\) qp with (rationally independent) frequencies \(\omega_1,\dots, \omega_r\) and absolutely convergent Fourier ...
Küpper, Tassilo, Yuan, Rong
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Вестник КазНУ. Серия математика, механика, информатика, 2022 In this paper, modification of Dzhumabaev parameterization method is developed to a boundary value problem for systems of loaded differential equations with piecewise constant argument of generalized type (EPCAG).
E. Bakirova +2 more
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Singularly perturbed linear oscillator with piecewise-constant argument
Вестник КазНУ. Серия математика, механика, информатика, 2018 The Cauchy problem for singularly perturbed linear differential equation the second order with piecewise-constant argument is considered in the article.
M. U. Akhmet +3 more
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Modeling a Tumor Growth with Piecewise Constant Arguments [PDF]
Discrete Dynamics in Nature and Society, 2013 Summary: This study is based on an early brain tumor growth that is modeled as a hybrid system such as (A): \(dx(t)/dt = x(t)\{r(1 - \alpha x(t) - \beta_0 x([ \! [t] \! ]) - \beta_1 x([ \! [t - 1] \! ])) + \gamma_1 x([ \! [t] \! ]) + \gamma_2 x ([ \! [t - 1] \! ])\}\), where the parameters \(\alpha, \beta_0, \beta_1\), and \(r\) denote positive numbers,
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