Pseudo almost periodic solutions for CNNs with leakage delays and complex deviating arguments

Abstract

In this paper, cellular neural networks with leakage delays and complex deviating arguments are considered. Some criteria are established for the existence of pseudo almost periodic solutions for this model by using the exponential dichotomy theory, contraction mapping fixed point theorem and inequality analysis technique. The results of this paper are new and complement previously known results.

Pseudo Almost Periodic Solutions for SICNNs with Leakage Delays and Complex Deviating Arguments

“…We also mention that all results in the references [6][7][8][15][16][17][18][19][20]23,24] cannot be directly applied to imply the existence of pseudo almost periodic solutions to (4.1) and (4.2). Here we present a novel proof to establish some criteria to guarantee the existence of pseudo almost periodic solutions for SICNNs with leakage delays and complex deviating arguments.…”

Weighted pseudo-almost periodic solutions and global exponential synchronization for delayed QVCNNs

“…Cellular neural networks (CNNs), which were originally proposed by Chua and Yang in [1,2], have been widely used in signal processing, pattern recognition, associative memory, combinatorial optimization, intelligent robot control, and other new fields of application are constantly being discovered. In the past 30 years, many authors have considered the existence, uniqueness and stability of equilibrium points ( [3]), periodic solutions ( [4,5]), almost periodic solutions ( [6,7]), pseudo-almost periodic solutions ( [8,9]) and weighted pseudo-almost periodic solutions ( [10,11]) of CNNs. In addition, as is well known, for artificial neural network systems and theoretical ecosystems, the dynamic behavior of the systems is the focus of great concern and interest.…”

“…Therefore, system (1) and system (9) are globally exponentially synchronized. This completes the proof.…”

New studies on dynamic analysis of asymptotically almost periodic recurrent neural networks involving mixed delays

“…Particularly, (asymptotically, pseudo) almost neural networks have received great deal of attention in the past decade due to their potential applications in classification, associative memory parallel computation, and other fields. So there have been many research results about the almost periodicity [13][14][15][16][17][18][19], pseudo almost periodicity [20][21][22][23][24][25][26][27][28], and weighted pseudo almost periodicity [29][30][31][32] on neural networks. From the viewpoint of mathematics, let (x 1 (t), x 2 (t), .…”

“…Further information on the mixed delays and coefficient parameters is available from [1,13,14]. Recently, for b i (u) = u (i ∈ S), by using the exponential dichotomy theorem in semilinear differential systems, the almost periodicity and pseudo almost periodicity have been fully investigated in [15][16][17][18][19] and [20][21][22][23][24][25][26][27][28][29][30][31][32], respectively. Nevertheless, as a nonlinear differential equation, RNNs (1.1) involving that b i (u) = u for some i ∈ S has no exponential dichotomy, and there are a few research works on the asymptotically almost periodicity analysis for this case.…”