Shunting Inhibitory Cellular Neural Networks Research Articles

Mean-squared exponential stability of distributed almost periodic sequence for nonlocal space-time discrete shunting inhibitory cellular neural networks with Brownian motions

The discrete-time and discrete-space model for stochastic nonlocal shunting inhibitory cellular neural networks with reaction diffusions are modelled in the first time. Owing to the consideration of spatial variables, the discrete model derived in this article is more complex than the traditional ordinary difference model. In accordance with the constant-variation-formula for discrete-time and discrete-space model, Banach contracting mapping principle, the method of proof by contradiction and stochastic calculus, we also obtain the existence of a unique bounded almost periodic sequence for the discrete model, which is exponentially stable in the mean-square sense. Noting that it is the first time to consider the dynamics of almost periodicity in distribution of time-space discrete neural network models. The practicability of the present results is demonstrated by means of an illustration.

B‐almost periodic solutions in finite‐dimensional distributions for octonion‐valued stochastic shunting inhibitory cellular neural networks

In this paper, we consider a class of octonion‐valued stochastic shunting inhibitory cellular neural networks with delays. First, we give an estimate of the distance between two different moments of finite‐dimensional distributions of a stochastic process. Then, based on this and by using fixed point theorems and inequality techniques, we establish the existence and global exponential stability of Besicovitch almost periodic ( ‐almost periodic for short) solutions in finite‐dimensional distributions for this kind of networks. Our results are new even if the networks we consider in the paper are real‐valued ones. At the same time, the method proposed in this paper can be applied to study the existence of Besicovitch almost periodic solutions in finite‐dimensional distributions for other types of stochastic neural networks. Finally, an example is given to illustrate the effectiveness of our results.

Almost periodic solutions for Clifford-valued stochastic shunting inhibitory cellular neural networks with mixed delays

<abstract><p>We adopted a non decomposition method to study the existence and stability of Stepanov almost periodic solutions in the distribution sense of stochastic shunting inhibitory cellular neural networks (SICNNs) with mixed time delays. Due to the lack of linear structure in the set composed of Stepanov almost periodic stochastic processes in the distribution sense. Due to the lack of linear structure in the set composed of distributed Stepanov periodic stochastic processes, it poses difficulties for the existence of Stepanov almost periodic solutions in the distribution sense of SICNNs. To overcome this difficulty, we first proved that the network under consideration has a unique solution in a space composed of $ \mathcal{L}^p $ bounded and $ \mathcal{L}^p $ uniformly continuous stochastic processes. Then, using stochastic analysis, inequality techniques, and the definition of Stepanov almost periodic stochastic processes in the distribution sense, we proved that this solution is also a Stepanov almost periodic solution in the distribution sense. Moreover, the result of the global exponential stability of this almost periodic solution is given. It is worth noting that even if the network under consideration degenerated into a real-valued network, our results are novel. Finally, we provided a numerical example to validate our theoretical findings.</p></abstract>

Finite-time/fixed-time synchronization of memristive shunting inhibitory cellular neural networks via sliding mode control

This paper proposes a novel time-dependent gain parameter-based sliding mode controller (SMC) to realize the finite-time/fixed-time synchronization of memristive shunting inhibitory cellular neural networks (Mem-SICNNs) having time-varying delays. In this regard, a new terminal sliding mode surface is designed and its reachability is analyzed. According to synchronization error analysis, the stability property of the desired error system is reached within finite-time/fixed-time range by proposing a unique time-dependent gain parameter-based SMC and choosing the appropriate Lyapunov functionals. Finally, a numerical example is approached by software simulation and manual calculation to estimate the settling-time of the finite-time/fixed-time synchronization criteria of the proposed Mem-SICNNs model.

Shunting Inhibitory Cellular Neural Networks with Compartmental Unpredictable Coefficients and Inputs

Shunting inhibitory cellular neural networks with compartmental periodic unpredictable coefficients and inputs is the focus of this research. A new algorithm is suggested, to enlarge the set of known unpredictable functions by applying diagonalization in arguments of functions of several variables. Sufficient conditions for the existence and uniqueness of exponentially stable unpredictable and Poisson stable outputs are obtained. To attain theoretical results, the included intervals method and the contraction mapping principle are used. Appropriate examples with numerical simulations that support the theoretical results are provided. It is shown how dynamics of the neural network depend on a new numerical characteristic, the degree of periodicity.

Equilibrium point, exponential stability and synchronization of numerical fractional-order shunting inhibitory cellular neural networks with piecewise feature

In recent years, exponential Euler difference methods for first-order semi-linear differential equations have been developed rapidly, and various exponential Euler difference methods have become a very important research topic. For fractional-order shunting inhibitory cellular neural networks with time lags, this article first establishes a new difference method named Mittag-Leffler Euler difference, which includes exponential Euler difference. Second, the existence of unique global bounded solution and equilibrium point, exponential stability and synchronization of the derived difference model are investigated. Compared with the classical fractional-order Euler difference method, the Mittag-Leffler discrete shunting inhibitory cellular neural networks can better describe and maintain the dynamic properties of the corresponding continuous-time models. More importantly, it opens up a new way to study discrete-time fractional-order systems and establishes a set of theory and methods to study Mittag-Leffler discrete neural networks.

Poisson Stability in Symmetrical Impulsive Shunting Inhibitory Cellular Neural Networks with Generalized Piecewise Constant Argument

In the paper, shunting inhibitory cellular neural networks with impulses and the generalized piecewise constant argument are under discussion. The main modeling novelty is that the impulsive part of the systems is symmetrical to the differential part. Moreover, the model depends not only on the continuous time, but also the generalized piecewise constant argument. The process is subdued to Poisson stable inputs, which cause the new type of recurrent signals. The method of included intervals, recently introduced approach of recurrent motions checking, is effectively utilized. The existence and asymptotic properties of the unique Poisson stable motion are investigated. Simulation examples for results are provided. Finally, comparing impulsive shunting inhibitory cellular neural networks with former neural network models, we discuss the significance of the components of our model.

Dynamics of Shunting Inhibitory Cellular Neural Networks with Variable Two-Component Passive Decay Rates and Poisson Stable Inputs

Shunting inhibitory cellular neural networks with continuous time-varying rates and inputs are the focus of this research. A new model is considered with compartmental passive decay rates which consist of periodic and Poisson stable components. The first component guarantees the Poisson stability of the dynamics, and the second one causes irregular oscillations. The inputs are Poisson stable to take into account the more sophisticated environment of the networks. The rates and inputs are synchronized to obtain Poisson stable outputs. A new efficient technique for checking the recurrence, the method of included intervals, is applied. Sufficient conditions for the existence of a Poisson stable solution and its asymptotic stability were obtained. Numerical simulations of Poisson stable outputs as well as inputs are provided. Examples of the model with Poisson stable rates, inputs and outputs confirm the feasibility of theoretical results. Discussions were undertaken to provide additional light on the relation of the obtained results with practical and theoretical potentials of neuroscience. Quantitative characteristics are suggested, which can be useful for the future applications of the results. In particular, the center of antisymmetry for the degree of periodicity is determined.

Finite-time and fixed-time synchronization analysis of shunting inhibitory memristive neural networks with time-varying delays

In the present paper, we investigate both the finite-time and fixed-time synchronization of retarded shunting inhibitory cellular neural networks. By constructing suitable Lyapunov functions and feedback control schemes we derive several sufficient conditions to guarantee finite-time and fixed-time synchronization of such networks. Finally, to illustrate the effectiveness of our theoretical results we consider examples with numerical simulations.

Weyl almost periodic solutions for quaternion-valued shunting inhibitory cellular neural networks with time-varying delays

<abstract><p>We consider the existence and stability of Weyl almost periodic solutions for a class of quaternion-valued shunting inhibitory cellular neural networks with time-varying delays. In order to overcome the incompleteness of the space composed of Weyl almost periodic functions, we first obtain the existence of a bounded continuous solution of the system under consideration by using the fixed point theorem, and then prove that the bounded solution is Weyl almost periodic by using a variant of Gronwall inequality. Then we study the global exponential stability of the Weyl almost periodic solution by using the inequality technique. Even when the system we consider degenerates into a real-valued one, our results are new. A numerical example is given to illustrate the feasibility of our results.</p></abstract>

Unpredictable oscillations of SICNNs with delay

We rigorously prove that unpredictable oscillations take place in the dynamics of shunting inhibitory cellular neural networks (SICNNs) with delay when rectangular input currents generated by an unpredictable sequence are utilized. The existence, uniqueness, and exponential stability of such oscillations are discussed. The contraction mapping principle is applied to achieve the theoretical results. Numerical simulations supporting the presence of unpredictable oscillations are provided, and the transfer of unpredictable behavior between SICNNs under unidirectional coupling is demonstrated. It is also shown by means of the delayed feedback control method that the obtained unpredictable behavior is controllable. Moreover, an application to secure communication is discussed.

Global Lagrange stability analysis of retarded SICNNs

Abstract The stability in the Lagrange sense for cellular neural networks (CNNs) has proven to be one of the effective tools to study multi-stable dynamics of the neural networks. In this article, rather than studying the existence and Lyapunov stability of an equilibrium point we investigate multi-stable dynamics of shunting inhibitory cellular neural networks (SICNNs) with time-varying delays and coefficients. This is the first paper that addresses the Lagrange stability for SICNNs. By constructing proper Lyapunov functions and using inequality techniques, we analyze three different types of activation functions, namely, bounded, sigmoid and Lipschitz-like type activation functions. New delay-dependent sufficient criteria are derived to ensure the global Lagrange stability for SICNNs. Furthermore, globally exponentially attractive sets are given for the different activation functions. Finally, an illustrating example with numerical simulations is given to support the theoretical results.

New convergence results on cellular neural networks with leakage delay and proportional delay

In the present work, we mainly focus on shunting inhibitory cellular neural networks (SICNNs) involving leakage delays and proportional delays. By applying the inequality technique, a novel sufficient criterion to ascertain the convergence of every solution of SICNNs with leakage delays and proportional delays is derived. Simulation results are delineated to substantiate the correctness of our theoretical findings. Up to now, very few scholars deal with the neural networks with leakage delays and proportional delays. The derived conclusion of this work is a novelty and supplements several earlier works.

Weighted pseudo almost periodicity of multi-proportional delayed shunting inhibitory cellular neural networks with D operator

Taking into account the effects of multi-proportional delays and D operator, this paper investigates the stability issue of a general class of neutral-type SICNNs (shunting inhibitory cellular neural networks). With the help of fixed point theorem and some novel differential inequality techniques, we derive a new sufficient conditions to ensure the existence, uniqueness and exponential stability of weighted pseudo almost periodic solutions (WPAPS) of the considered model. The obtained main results are totally new and generalize some published results. At the end of this work, we also give some numerical simulations to support the proposed approach and demonstrate the correctness of the main conclusions.

Shunting inhibitory cellular neural networks with strongly unpredictable oscillations

The paper considers a new type of solutions for shunting inhibitory cellular neural networks (SICNNs), strongly unpredictable oscillations. The conditions for the existence, uniqueness and stability of the solutions are determined. Numerical examples are given to show the feasibility of the obtained results.

Mean almost periodicity and moment exponential stability of discrete-time stochastic shunting inhibitory cellular neural networks with time delays

Mean almost periodicity and moment exponential stability of discrete-time stochastic shunting inhibitory cellular neural networks with time delays

Influence of time delay on weighted pseudo-almost periodic dynamics in SICNNs

PurposeThe purpose of this paper is to investigate the weighted pseudo-almost periodic solutions of shunting inhibitory cellular neural networks (SICNNs) with time-varying delays and distributed delays.Design/methodology/approachThe principle of weighted pseudo-almost periodic functions and some new mathematical analysis skills are applied.FindingsA set of sufficient criteria which guarantee the existence and exponential stability of the weighted pseudo-almost periodic solutions of the considered SICNNs are established.Originality/valueThe derived results of this paper are new and complement some earlier works. The innovation of this paper concludes two points: a new sufficient criteria guaranteeing the existence and exponential stability of the weighted pseudo-almost periodic solutions of SICNNs are established; and the ideas of this paper can be applied to investigate some other similar neural networks.

Dynamics of anti-periodic solutions on shunting inhibitory cellular neural networks with multi-proportional delays

Since proportional delay is monotonically increasing, a neural network involving multi-proportional delays is obviously not anti-periodic, yet a very interesting fact in this paper shows that it is possible there is an anti-periodic solution for such systems. This paper aims to deal with the issue of anti-periodic solutions for SICNNs (Shunting Inhibitory Cellular Neural Networks) involving multi-proportional delays. With the help of Lyapunov method, inequality techniques and a concise mathematical analysis proof, sufficient criteria on the existence of anti-periodic solutions including its uniqueness and exponential stability are established. The obtained results provide us some lights for designing a stable SICNNs and complement some earlier publications. Furthermore, simulations show that the theoretical anti-periodic dynamics are in excellent agreement with the numerically observed behavior.

Measure Pseudo Almost Periodic Solutions of Shunting Inhibitory Cellular Neural Networks with Mixed Delays

In this work, we consider a class of neutral shunting inhibitory cellular neural networks with mixed delays. We study the existence, uniqueness, and the exponential stability of the measure pseudo almost periodic (or μ-pseudo almost periodic) solutions from some models for shunting inhibitory cellular neural networks with mixed delays. An example is provided to illustrate the theory developed in this work.

Weighted Pseudo Almost Periodic Shunting Inhibitory Cellular Neural Networks with Multi-proportional Delays

In this present paper, the dynamics of weighted pseudo almost periodic shunting inhibitory cellular neural networks with multi-proportional delays is concerned. By applying the fixed point theorem and differential inequality techniques, the existence and global exponential stability of weighted pseudo almost periodic solutions for the addressed model are investigated, which are completely new and extend previously known studies. Furthermore, an example with graphical illustration is given to illustrate the effectiveness of the theoretical results.