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This article investigates quaternion-valued fuzzy cellular neural networks with delays. With the help of fixed point theory, exponential dichotomy of linear equations and related inequalities, some new sufficient conditions which guarantee the existence and global exponentially stability of pseudo almost periodic solutions to quaternion-valued fuzzy cellular neural networks with delays are established. Computer simulations are carried out to check the practicability of the obtained main results. So far, no researchers have investigated this topic. The derived results of this article are completely innovative and complement some earlier investigations to some degree.

The stability and Hopf bifurcation have important effect on the design of neural networks. By revealing the effect of parameters on the stability and Hopf bifurcation of neural networks, we can better apply neural networks to serve humanity. This article is principally concerned with the stability and the emergence of Hopf bifurcation of fractional-order BAM neural networks with multiple delays. Applying Laplace transform, stability theory and Hopf bifurcation knowledge of fractional-order differential systems, we establish a new sufficient condition to ensure the stability and the emergence of Hopf bifurcation of the addressed fractional-order BAM neural networks with multiple delays. The research indicates that the delay has a vital effect on the stability and the appearance of Hopf bifurcation of fractional-order BAM neural networks. Computer simulations are put into effect to test the effectiveness of the theoretical findings. It is shown that when the sum of time delays crosses some critical values, the stability of networks loses and Hopf bifurcation will happen.

Coordination of identical metals has significant impact on catalytic activity and selectivity of heterogeneous catalyst. Here, we show that the selectivity for hydrogenation of Pd can be manipulated by altering the coordinate environment. PdNi/SiO2 dilute alloy nanocatalysts have been synthesized at room temperature, which show effectively the unparalleled catalytic performance (about 100% selectivity to styrene) for phenylacetylene hydrogenation at 30 °C with full conversion. Structural and surface analyses show that the improvement in dispersion of the Pd active sites and the changed electronic structure of Pd contribute the catalytic performance significantly. This work is an important step towards developing highly active hydrogenation catalysts by forming dilute alloys.

In the present work, new fractional order BAM neural networks with multiple delays are formulated. Firstly, we study the existence and uniqueness of solution of the constructed neural networks by applying Lipschitz condition. Secondly, the boundedness of solution for the involved neural networks is analyzed by constructing an appropriate function. Thirdly, with the aid of the stability theorem and Hopf bifurcation theory of the fractional order delayed differential systems, the sufficient criterion to guarantee the stability and the existence of Hopf bifurcation for the addressed neural networks is set up. In the end, simulation results are displayed with computer software to support research findings. The established theoretical results of this work have significant theoretical guiding value in dominating and optimizing networks.

Noble metals are downsized to nano-/subnano-scale to improve their catalytic activity and atom-economy. However, the stabilities in chemical state and catalytic performance of these nanocatalysts often suffer during harsh conditions. For Pt nanoparticles (NPs) supported on CeO2, activated oxygen diffused from the support over-stabilizes the active sites of Pt, degrading its performance at mild temperature. In this work, Pt nanocatalysts with unique structure of triple-junction are synthesized by selectively growing Pt NPs on the carbon-CeO2 interface. Impressively, the Pt NPs exhibit much enhanced catalytic stability and high activity for CO oxidation at mild temperature. The enhancement is attributed to electron donation from graphitized carbon and the confinement effect from the high-density nanopores of the CeO2 support. The triple-junction of Pt-C-CeO2, combining the merits of CeO2 for activating O2 and electron donating capability of carbon, provides new inspiration to the fabrication of high-performance nanocatalysts.

The interface between metal nanoparticles (NPs) and support plays a vital role in catalysis because both electron and atom exchanges occur across the metal-support interface. However, the rational design of interfacial structure facilitating the charge transfer between the neighboring parts remains a challenge. Herein, a guided nucleation strategy based on redox reaction between noble metal precursor and support-surface is introduced to construct epitaxial interfaces between Pt NPs and CeO2 support. The Pt/CeO2 catalyst exhibits near room temperature catalytic activity for CO oxidation that is benefited from the well-defined interface structure facilitating charge transfer from CeO2 support to Pt NPs. Meanwhile, this general approach based on support-surface-induced-nucleation was successfully extended to synthesize Pd and Cu nanocatalysts on CeO2, demonstrating its universal and feasible characteristics. This work is an important step towards developing highly active supported metal catalysts by engineering their interfaces.

In this manuscript, fuzzy delayed cellular neural networks with impulse are studied. Applying time scale calculus knowledge, mathematical inequalities and constructing Lyapunov function, we establish a sufficient criterion that guarantees the existence and exponential stability of anti-periodic solutions for fuzzy delayed cellular neural networks with impulse. In addition, an example with its numerical simulations is given to illustrate our theoretical predictions.

In this article, on the basis of predecessors, works, we will propose a new fractional-order neural network model with multiple delays. Letting two different delays be bifurcation parameters and analyzing the corresponding characteristic equations of considered model, we will establish a set of new sufficient criteria to guarantee the stability and the appearance of Hopf bifurcation of fractional-order network model with multiple delays. The impact of two different delays on the stability behavior and the emergence of Hopf bifurcation of involved network model is revealed. The influence of the fractional order on the stability and Hopf bifurcation of involved model is also displayed. To check the correctness of analytical results, we perform programmer simulations with software. A conclusion is drawn in the end. The analysis results in this article are innovative and have important theoretical significance in designing neural networks.

In this paper, based on the earlier research, a new fractional-order chaotic Genesio-Tesi model is established. The chaotic phenomenon of the fractional-order chaotic Genesio-Tesi model is controlled by designing two suitable time-delayed feedback controllers. With the aid of Laplace transform, we obtain the characteristic equation of the controlled chaotic Genesio-Tesi model. Then by regarding the time delay as the bifurcation parameter and analyzing the characteristic equation, some new sufficient criteria to guarantee the stability and the existence of Hopf bifurcation for the controlled fractional-order chaotic Genesio-Tesi model are derived. The research shows that when time delay remains in some interval, the equilibrium point of the controlled chaotic Genesio-Tesi model is stable and a Hopf bifurcation will happen when the time delay crosses a critical value. The effect of the time delay on the stability and the existence of Hopf bifurcation for the controlled fractional-order chaotic Genesio-Tesi model is shown. At last, computer simulations check the rationalization of the obtained theoretical prediction. The derived key results in this paper play an important role in controlling the chaotic behavior of many other differential chaotic systems.

Purpose The 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/approach The principle of weighted pseudo-almost periodic functions and some new mathematical analysis skills are applied. Findings A 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/value The 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.

This article mainly studies delayed fuzzy cellular neural networks. A sufficient criterion to guarantee the existence and exponential stability of anti-periodic solutions for this system is given. ...

The paper deals with the stability and bifurcation analysis of a class of simplified five-neuron bidirectional associative memory neural networks with four delays. By discussing the characteristic transcendental equation and applying Hopf bifurcation theory, some sufficient conditions which guarantee the local stability and the existence of Hopf bifurcation of the neural networks are established. With the aid of the normal form theory and center manifold theory, we obtain some specific formulae to determine the stability and the direction of the Hopf bifurcation. Computer simulations are implemented to explain the key mathematical predictions. The paper ends with a brief conclusion.

Constructing materials with high-density interfaces offers a very promising route to enable high-performance nanocatalysts. Herein, a one-pot method to synthetize CuOx–CeO2 spherical catalysts with high-density interfaces is developed by controlling the growth condition so that the CuOx can only nucleate and grow via heterogeneous mode. The synthesis method ensures fine dispersion of CuOx over CeO2 and the density of interface between CuOx and CeO2. The generation of the species of Cu+, Ce3+, and oxygen vacancies are enhanced by the interface interaction. And the reduction of copper ions to metals is effectively suppressed, which helps to avoid deactivation of catalyst at high temperature. When catalyzing the CO preferential oxidation reaction (CO-PROX), the CuOx–CeO2 composite with high-density interfaces exhibits a strikingly high catalytic oxidation activity at a broad operating temperature window (i.e. CO 100% conversion, 95–235 °C). The heterogeneous nucleation methodology of synthesizing composite with high-density interfaces reported in this work also applies to other materials system.

In recent years, with the rapid development of the Internet and the Internet of Things, network security is urgently needed. Malware becomes a major threat to network security. Thus, the study on malware propagation model plays an important role in network security. In the past few decades, numerous researchers put up various kinds of malware propagation models to analyze the dynamic interaction. However, many works are only concerned with the integer-order malware propagation models, while the investigation on fractional-order ones is very few. In this paper, based on the earlier works, we will put up a new fractional-order delayed malware propagation model. Letting the delay be bifurcation parameter and analyzing the corresponding characteristic equations of considered system, we will establish a set of new sufficient conditions to guarantee the stability and the existence of Hopf bifurcation of fractional-order delayed malware propagation model. The study shows that the delay and the fractional order have important effect on the stability and Hopf bifurcation of considered system. To check the correctness of theoretical analyses, we carry out some computer simulations. At last, a simple conclusion is drawn. The derived results of this paper are completely innovative and play an important guiding role in network security.

Over the past several decades, numerous scholars have studied the stability and Hopf bifurcation problem of integer-order delayed neural networks. However, the fruits about the stability and Hopf bifurcation for fractional-order delayed neural networks are very scarce. In this paper, we will consider the stability and the existence of Hopf bifurcation of fractional-order bidirectional associative memory (BAM) neural networks with four delays. A set of sufficient criteria to ensure the stability and the existence of Hopf bifurcation for the fractional-order BAM neural networks with four delays are established by choosing the sum of two different delays as a bifurcation parameter. This paper manifests that the delay has an important influence on the stability and Hopf bifurcation of involved networks. An example is displayed to test the rationality of the derived theoretical findings. The derived results of this paper are new and play a key role in optimizing networks and improving human life.

In this manuscript, quaternion-valued delayed cellular neural networks are studied. Applying the continuation theorem of coincidence degree theory, inequality techniques and a Lyapunov function approach, a new sufficient condition that guarantees the existence and exponential stability of anti-periodic solutions for quaternion-valued delayed cellular neural networks is presented. The obtained results supplement some earlier publications that deal with the anti-periodic solutions of quaternion-valued neural networks with distributed delay or impulse or state-dependent delay or inertial term. Computer simulations are displayed to check the derived analytical results.

Over the past decades, many authors establish various kinds of competition and cooperation models of two enterprises to analyze the dynamic interaction. However, they are only concerned with integer-order differential equation models, while the reports on fractional-order ones are very rare. In this article, based on the earlier studies, we propose a new fractional-order delayed competition and cooperation model of two enterprises. Letting the delay be bifurcation parameter and analyzing the corresponding characteristic equation of involved model, we establish some new sufficient conditions to guarantee the stability and the existence of Hopf bifurcation of fractional-order delayed competition and cooperation model of two enterprises. The research indicates that different delays have different effect on the stability and Hopf bifurcation of involved model. The impact of the fractional order on the stability and Hopf bifurcation of involved model is displayed. To check the correctness of theoretical analysis, we implement some computer simulations.

This paper is concerned with fractional-order neural networks with proportional delays. Applying inequality technique, some sufficient criteria which ensure the stability of such fractional-order neural networks with proportional delays over a finite-time interval are established. Computer simulations are carried out to illustrate our theoretical predictions. The derived results of this paper are new and complement some earlier ones.

In this paper, fuzzy cellular neural networks with time-varying delays in leakage terms are investigated. With the help of the differential inequality theory and almost periodic function th...

Purpose The purpose of this paper is to investigate the existence and global exponential stability of periodic solution of memristor-based recurrent neural networks with time-varying delays and leakage delays. Design/methodology/approach The differential inequality theory and some novel mathematical analysis techniques are applied. Findings A set of sufficient conditions which guarantee the existence and global exponential stability of periodic solution of involved model is derived. Practical implications It plays an important role in designing the neural networks. Originality/value The obtained results of this paper are new and complement some previous studies. The innovation of this paper concludes two aspects: the analysis on the existence and global exponential stability of periodic solution of memristor-based recurrent neural networks with time-varying delays and leakage delays is first proposed; and it is first time to establish the sufficient criterion which ensures the existence and global exponential stability of periodic solution of memristor-based recurrent neural networks with time-varying delays and leakage delays.

In this paper, a class of simplified bidirectional associative memory (BAM) neural networks with multiple delays are considered. By analyzing the associated characteristic transcendental equation, their linear stability is investigated and Hopf bifurcation is demonstrated. By applying Nyquist criterion, the length of delay which preserves the stability of the zero equilibrium is estimated. Some explicit results are derived for stability and direction of the bifurcating periodic orbit by using the normal form theory and center manifold arguments. Global existence of periodic orbits is also established by using a global Hopf bifurcation theorem for functional differential equations (FDE) and a Bendixson’s criterion for high-dimensional ordinary differential equations (ODE) due to Li and Muldowney. Finally, numerical simulations supporting the theoretical analysis are carried out.

In this paper, a class of stochastic cellular neural networks with distributed delays are investigated. With the help of the method of variation parameter and inequality techniques, some sufficient conditions for the p-th moment exponential stability of the system are established. An example is given to illustrate the feasibility and effectiveness of our main results. Our results obtained in this paper improve and generalize some earlier works reported in the literature.

This paper deals with a class of memristor-based bidirectional associative memory (BAM) neural networks with leakage delays and time-varying delays. With the aid of the framework of Filippov solutions, Chain rule and some inequality techniques, a sufficient condition which ensures the boundedness and ultimate boundedness of solutions of memristor-based BAM neural networks with leakage delays and time-varying delays is established. Applying a new approach involving Yoshizawa-like theorem, we prove the existence of periodic solution of the memristor-based BAM neural networks. By using the theory of set-valued maps and functional differential inclusions, Lyapunov functional, a set of sufficient conditions which guarantee the uniqueness and global exponential stability of periodic solution of memristor-based BAM neural networks are derived. An example is given to illustrate the applicability and effectiveness of the theoretical predictions. The results obtained in this paper are completely new and complement the previously known studies of Li et al. [Existence and global exponential stability of periodic solution of memristor-based BAM neural networks with time-varying delays, Neural networks 75 (2016) 97-109.]

In this article, we discuss anti-periodic oscillations of BAM neural networks with leakage delays. A sufficient criterion guaranteeing the existence and exponential stability of the involved model is presented by utilizing mathematic analysis methods and Lyapunov ideas. The theoretical results of this article are novel and are a key supplement to some earlier studies.

The supports of copper slices with three-kind morphologies Cu 2 O layers were prepared by the hydrothermal method. The Cu 2 O layers are rod-like structure, three-dimensional reticular and porous morphology as well as flower-like morphology, respectively. The CeO 2 -CuO/Cu 2 O/Cu monolithic catalysts present porous and network structure or foam morphology after loading CeO 2 and CuO. Cu and Ce elements are uniformly dispersed onto the support surface. It is found that the monolithic catalyst with flower-like Cu 2 O layer displays better low-temperature activity because of highly-dispersed CuO and high O latt concentration. The monolithic catalysts with rod-like or reticular-morphology Cu 2 O layers present high-temperature activity due to larger CuO crystallite sizes and good synergistic effect at copper-ceria interfacial sites. The as-prepared CeO 2 -CuO/Cu 2 O/Cu monolithic catalysts show good performance in the CO-PROX reaction. The generation of Cu 2 O layers with three-kind morphologies is beneficial to the loading and dispersion of copper oxides and ceria.

In this paper, shunting inhibitory cellular neural networks(SICNNs) with time-varying delays in leakage terms on time scales are investigated. With the aid of the existence of the exponential dichotomy of linear dynamic equations on time scales, fixed point theorem and the theory of calculus on time scales, we establish some sufficient conditions to ensure the existence and exponential stability of almost automorphic solutions for the model. An example with its numerical simulations is given to illustrate the feasibility and effectiveness of the theoretical findings.

This paper deals with a class of neutral shunting inhibitory cellular neural networks with time-varying delays and D operator. Using the differential inequality theory and Lyapunov functional method, a set of sufficient conditions which ascertains that the existence and exponential stability of anti-periodic solutions of neutral shunting inhibitory cellular neural networks with time-varying delays and D operator are derived. Computer simulations are delineated to substantiate the correctness of our theoretical predictions. The obtained results of this paper are new and complement some earlier works.

This study mainly explores fractional-order six-neuron bi-directional associative memory (BAM) neural networks involving multi-delays. Taking advantage of contraction mapping principle, we prove that the solution of the addressed BAM neural networks exists and is unique. Utilizing a acceptable function, we confirm that the solution of the addressed BAM neural networks is bounded. By applying a suitable variable substitution, new fractional order six-neuron BAM neural networks involving mult-delays are converted to a class of fractional order six-neuron BAM neural networks with single delay. Using the stability criterion and bifurcation theory of fractional order differential dynamical systems, we carry out a detailed discussion on the stability and the onset of Hopf bifurcation of the established BAM neural networks. The study shows that the time delay is an important factor which affects the stability behavior and Hopf bifurcation of the involved neural networks. Numerical simulation plots are presented to illustrate our derived key conclusions. The derived analytical findings of the study play a vital role in optimizing and designing neural networks.

The RGO/MWCNTs/Cu x O-CeO 2 catalysts were synthesized by the precipitation and hydrothermal method, respectively. They were characterized via SEM, XRD, H 2 -TPR, XPS and N 2 adsorption-desorption techniques. It is found that the particles of Cu x O and CeO 2 are dispersed on the RGO sheets. The MWCNTs enter the two-dimension RGO interconnected network and play the role of spacer between RGO sheets. The introduction of RGO and MWCNTs improves the dispersion and the reduction of Cu x O and CeO 2 , and increases the concentration of oxygen vacancies. These improvements enhance the activity of the catalysts at low temperature.

In this paper, stochastic fuzzy Cohen–Grossberg neural networks with discrete and distributed delays are investigated. By using Lyapunov function and the Ito differential formula, some sufficient conditions for the pth moment exponential stability of such stochastic fuzzy Cohen–Grossberg neural networks with discrete and distributed delays are established. An example is given to illustrate the feasibility of our main theoretical findings. Finally, the paper ends with a brief conclusion. Methodology and achieved results is to be presented.

The sheet-on-sheet reduced graphene oxide (RGO)/Cu x O CeO 2 catalysts were synthesized by a facile hydrothermal procedure and systematically characterized by X-ray powder diffraction, scanning electron microscopy, transmission electron microscopy, hydrogen temperature-programmed reduction, X-ray photoelectron spectroscopy and N 2 adsorption–desorption techniques. It is found that there is a large amount of reduced copper species in the RGO/Cu x O CeO 2 catalysts, and the addition of RGO was beneficial for the dispersion of particles and the improvement of textural properties. The spherical nanoparticles of copper species can be served as spacers to prevent the stacking of RGO. Copper and cerium species are homogenously distributed on the surface of RGO sheets. The introduction of RGO improves the formation of high Ce 3+ concentration and oxygen vacancies. Therefore, the RGO/Cu x O CeO 2 catalysts show higher catalytic activity than the CuO CeO 2 catalyst at low temperature (below 135 °C). Moreover, good resistance to H 2 O and CO 2 of the RGO/Cu x O CeO 2 may be from for the formation of hydroxyl groups by dissociative adsorption of H 2 O on the surface of RGO, which can improve the WGS reaction and the decomposition of carbonates.

In this paper, a class of fuzzy cellular neural networks (FCNNs) with leakage delays, distributed delays and proportional delays are considered. Using the differential inequality strategy, some sufficient criteria which ensure the global exponential convergence of the FCNNs with leakage delays, distributed delays and proportional delays are established. Numerical simulations are given to explain the obtained analytical results. The derived conclusions of this article are new and complement some earlier publications.

This paper is concerned with a class of neutral-type Hopfield neural networks with multi-proportional delays and leakage delays. Using the differential inequality theory, a set of sufficient conditions which guarantee that all solutions of neutral-type Hopfield neural networks with multi-proportional delays and leakage delays converge exponentially to zero vector are derived. Computer simulations are carried out to verify our theoretical findings. The obtained results of this paper are new and complement some previous studies.

In this letter, we deal with a class of memristor-based neural networks with distributed leakage delays. By applying a new Lyapunov function method, we obtain some sufficient conditions that ensure the existence, uniqueness, and global exponential stability of almost periodic solutions of neural networks. We apply the results of this solution to prove the existence and stability of periodic solutions for this delayed neural network with periodic coefficients. We then provide an example to illustrate the effectiveness of the theoretical results. Our results are completely new and complement the previous studies Chen, Zeng, and Jiang ( 2014 ) and Jiang, Zeng, and Chen ( 2015 ).

In this paper, high-order Hopfield neural networks with time-varying leakage delays are investigated. By applying Lyapunov functional method and differential inequality techniques, a set of sufficient conditions are obtained for the existence and exponential stability of pseudo almost periodic solutions of the model. Some simulations are carried out to support the theoretical findings. Our results improve and generalize those of the previous studies.

Background Although the amount of research work on bifurcation analysis of neural networks is growing explosively, the majority of such research effort is devoted to bifurcation of neural networks with discrete delays, while efficient detection of Hopf bifurcation phenomena in neural networks with distributed delays remains a challenging task. The aim of this study is to determine the effect of time delay on the dynamical behavior of two-neuron networks with discrete and distributed delays.

This paper is concerned with interval general bidirectional associative memory (BAM) neural networks with proportional delays. Using appropriate nonlinear variable transformations, the interval general BAM neural networks with proportional delays can be equivalently transformed into the interval general BAM neural networks with constant delays. The sufficient condition for the existence and uniqueness of equilibrium point of the model is established by applying Brouwer's fixed point theorem. By constructing suitable delay differential inequalities, some sufficient conditions for the global exponential stability of the model are obtained. Two examples are given to illustrate the effectiveness of the obtained results. This paper ends with a brief conclusion. Copyright © 2016 John Wiley & Sons, Ltd.

Three-dimensionally ordered macroporous CeO2–CuO catalysts were prepared by the template and sol–gel method. The catalysts were characterized via SEM, TEM, XRD, H2-TPR, XPS, CO2-TPD and N2 adsorption–desorption techniques. It is found that the CeO2–CuO catalysts present the well-defined interconnected macroporous structure in three dimensions, and the skeleton of macroporous structure is composed of the CuO and CeO2 particles. Catalytic performance for preferential CO oxidation is determined by various properties including composition, structural and textural properties as well as reduction and desorption behavior. The 3DOM CeO2–CuO structure improves the interaction between CuO and CeO2, the structural and textural properties, the reduction of oxides and desorption of the adsorbed molecules on the active sites.

The Cu x O-CeO 2 /Fe@CNSs, Cu x O-CeO 2 /MWCNTs-Co and Cu x O-CeO 2 /MWCNTs-Ni catalysts were prepared by the impregnation method and characterized by transmission electron microscopy, scanning electron microscopy, X-ray powder diffraction, H 2 -temperature programmed reduction and N 2 adsorption-desorption techniques. It was found that the Fe nanoparticles were encapsulated into the multi-layered carbon nanospheres (CNSs). However, the multi-wall carbon nanotubes (MWCNTS) were generated on the Co/Al 2 O 3 and Ni/Al 2 O 3 precursor. The addition of carbon nanomaterial as supports could improve structural properties and low-temperature activity of the CuO-CeO 2 catalyst, and save the used amount of metal catalysts in the temperature range with high selectivity for CO oxidation. The copper-cerium oxides supported on carbon nanomaterial had good resistence to H 2 O and CO 2 .

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.

In this article, a kind of fuzzy cellular neural networks (FCNNs) with proportional delays and leakage delays are involved. Utilizing the differential inequality strategies, a sequence of sufficient criteria ensuring the global exponential convergence of involved model are presented. Computer simulations are performed to verify the analytic findings. The analytic findings of this article are innovative and complete several existing works.

In this paper, a three-neuron artificial neural network model with distributed delays is considered. Its dynamics is investigated in term of the linear stability analysis and Hopf bifurcation analysis. By regarding the sum of two delays as a bifurcation parameter and analyzing the associated characteristic equation, we find that Hopf bifurcation occurs when the bifurcation parameter passes through some certain values. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions are derived by using the normal form method and center manifold theory. Finally, computer simulations are given to support the theoretical predictions.

Bidirectional associative memory (BAM) networks play an important role in various fields such as optimization, pattern recognition, classification, signal and image processing, parallel computation and associative memory. In this paper, four-neuron BAM networks with inertia and multiple delays are considered. By analyzing the distribution of the eigenvalues of the associated characteristic transcendental equation, local stability criteria are obtained for various system parameters and time delays. By choosing the sum of time delays as a bifurcation parameter, we found that Hopf bifurcation occurs when the sum of time delays passes through a sequence of critical values. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions are obtained by using the normal form theory and center manifold theory. Some numerical simulations are carried out to support theoretical predictions. Our results are new and supplement some previously known studies.

This paper is concerned with a class of fuzzy BAM cellular neural networks with distributed leakage delays and impulses. By applying differential inequality techniques, we establish some sufficient conditions which ensure the exponential stability of such fuzzy BAM cellular neural networks. An example is given to illustrate the effectiveness of the theoretical results. The results obtained in this article are completely new and complement the previously known studies.