This paper studies the general decay synchronization (GDS) of a class of recurrent neural networks (RNNs) with general activation functions and time-varying delays. By constructing suitable Lyapunov-Krasovskii functionals and employing useful inequality techniques, some sufficient conditions on the GDS of considered RNNs are established via a type of nonlinear control. In addition, an example with numerical simulations is presented to illustrate the obtained theoretical results.
This study investigates the dynamical behavior of a ratio-dependent Lotka–Volterra competitive-competitive-cooperative system with feedback controls and delays. Compared with previous studies, both ratio-dependent functional responses and time delays are considered. By employing the comparison method, the Lyapunov function method, and useful inequality techniques, some sufficient conditions on the permanence, periodic solution, and global attractivity for the considered system are derived. Finally, a numerical example is also presented to validate the practicability and feasibility of our proposed results.
A class of delayed spruce budworm population model is considered. Compared with previous studies, both autonomous and nonautonomous delayed spruce budworm population models are considered. By using the inequality techniques, continuation theorem, and the construction of suitable Lyapunov functional, we establish a set of easily verifiable sufficient conditions on the permanence, existence, and global attractivity of positive periodic solutions for the considered system. Finally, an example and its numerical simulation are given to illustrate our main results.
We studied a class of generalized n-species non-autonomous cooperative Lotka–Volterra (L-V) systems with time delays. We obtained new criteria on the dynamic properties of the systems. First, we obtained the boundedness and permanence of the system using the inequality analysis technique and comparison method. Then, the existence of positive periodic solutions was investigated using the coincidence degree theory. The global attractivity of the system was obtained by constructing suitable Lyapunov functionals and utilizing Barbalat’s lemma. The existence and global attractivity of the periodic solutions were also obtained. Finally, we conducted two numerical simulations to validate the feasibility and practicability of our results.
This paper studies the general decay synchronization (GDS) of a class of nonautonomous bidirectional associative memory recurrent neural networks (BAMRNNs) with mixed time delays. By employing the Lyapunov method and useful inequality techniques, some sufficient conditions on the general decay synchronization for BAMRNNs are derived. In addition, an example with numerical simulations is presented to illustrate the obtained theoretical results.
This paper studies a type of non-autonomous three-species Lotka-Volterra(L-V) predator-prey-competitive systems with time delays is discussed. Several sufficient conditions on the global attractivity of the system are derived by employing the Lyapunov function method.
This paper investigates the general decay synchronization (GDS) for fuzzy cellular neural networks (FCNNs). Compared with previous research results, constant time delays and distributed time delays are taken into consideration. By using the Lyapunov function method and some inequality techniques, several sufficient conditions are derived on the GDS for FCNNs. Ultimately, a numerical example is also carried out to validate the practicability and feasibility of our proposed results.
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