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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.

In this paper, a Kaldor-Kalecki business cycle model with double delays is considered. By using the stability theory and bifurcation theory of functional differential equations, we obtain the local stability and the conditions of Hopf bifurcation of the system at the equilibrium point. We focus on the impact of consumption delay and investment delay on stability, respectively. Finally, the results of theoretical analysis are verified by some numerical simulations.

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.

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.

In this article, based on the previous works, a new fractional-order financial model is put up. The chaotic behavior of the fractional-order financial model is suppressed by designing an appropriatePDϑcontroller. By choosing the delay as the bifurcation parameter, we establish the sufficient condition to guarantee the stability and the existence of Hopf bifurcation of fractional-order financial model. Also, the influence of the delay and the fractional order on the stability and the existence of Hopf bifurcation of fractional-order financial model is revealed. An example is given to confirm the effectiveness of the analysis results. The main findings of this article play an important role in maintaining economic stability.

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 this paper, we put up and study a competition and cooperation model of two enterprises with multiple delays and feedback controls. A set of sufficient conditions which ensure the existence of periodic solution of the two-enterprise competition and cooperation model with multiple delays and feedback controls are established by applying the fixed point theorem of strict-set-contraction. An example is given to check the obtained theoretical findings. The derived results are completely new and complement earlier publications.

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.

In today’s society, the Internet has become an important tool of our life due to its potential applications in various areas such as economics, industry, agriculture, medical and health care, and information processing. To understand and grasp the law of the Internet, many competitive web site models of the Internet and some phenomena related to World Wide Web have been investigated systematically. However, many scholars only study the integer-order competitive web site models of the Internet. Up to now, there are few papers that focus on the dynamics of fractional-order competitive web site models of Internet, which possess memory property. In this paper, we are concerned with the stability and the existence of Hopf bifurcation of a fractional-order competitive web site model of Internet. By choosing the time delay as parameter and applying the Routh–Hurwitz criteria, we will establish a new sufficient condition guaranteeing the stability and the existence of Hopf bifurcation for fractional-order competitive web site model of Internet. The research reveals that fractional order and the delay play a key role in describing the stability and Hopf bifurcation of the considered system. Computer simulations are implemented to support the analytic results. Finally, a simple conclusion is presented. The theoretical findings of this article have a great significance in handling the competition dynamics among different web sites.

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 paper, we deal with a class of BAM neural networks with time-varying leakage delays. By applying the exponential dichotomy of linear differential equations, fixed point theorems and differential inequality techniques, we obtain some sufficient conditions which guarantee the existence and exponential stability of almost periodic solutions for such class of BAM neural networks. An example is provided to illustrate the effectiveness of the theoretical predictions. The results obtained in this paper are completely new and complement the previously known publications.

In this manuscript, a delayed Nicholson-type model with linear harvesting terms is investigated. Applying coincidence degree theory, we establish a sufficient condition which guarantees the existence of positive periodic solutions for the delayed Nicholson-type model. By constructing suitable Lyapunov functions, a new criterion for the uniqueness and global attractivity of the periodic solution of the Nicholson-type delay system is obtained. The derived results of this article are completely new and complement some previous investigations.

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.

In this paper, a discrete ratio-dependent food-chain system with delay is investigated. By using Gaines and Mawhin’s continuation theorem of coincidence degree theory and the method of Lyapunov function, a set of sufficient conditions for the existence of positive periodic solutions and global asymptotic stability of the model are established.

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 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.]

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 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.

Purpose The purpose of this paper is to study the existence and exponential stability of anti-periodic solutions of a class of shunting inhibitory cellular neural networks (SICNNs) with time-varying delays and continuously distributed delays. Design/methodology/approach The inequality technique and Lyapunov functional method are applied. Findings Sufficient conditions are obtained to ensure that all solutions of the networks converge exponentially to the anti-periodic solution, which are new and complement previously known results. Originality/value There are few papers that deal with the anti-periodic solutions of delayed SICNNs with the form negative feedback – aij(t)αij(xij(t)).

This paper deals with a stochastic two-species competitive model. Some very verifiable criteria on the global stability of the positive equilibrium of the deterministic system are established. An example with its computer simulations is given to illustrate our main theoretical findings.

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.