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This research paper conducts an investigation into the stability issue for a more general class of neutral-type Hopfield neural networks that involves multiple time delays in the states of neurons and multiple neutral delays in the time derivatives of the states of neurons. By constructing a new proper Lyapunov functional, an alternative easily verifiable algebraic criterion for global asymptotic stability of this type of Hopfield neural systems is derived. This new stability condition is entirely independent of time and neutral delays. Two instructive examples are employed to indicate that the result obtained in this paper reveals a new set of sufficient stability criteria when it is compared with the previously reported stability results. Therefore, the proposed stability result enlarges the application domain of Hopfield neural systems of neutral types.

This paper presents the multistability analysis and associative memory of neural networks (NNs) with Morita-like activation functions. In order to seek larger memory capacity, this paper proposes Morita-like activation functions. In a weakened condition, this paper shows that the NNs with n -neurons have ( 2 m + 1 ) n equilibrium points (Eps) and ( m + 1 ) n of them are locally exponentially stable, where the parameter m depends on the Morita-like activation functions, called Morita parameter. Also the attraction basins are estimated based on the state space partition. Moreover, this paper applies these NNs into associative memories (AMs). Compared with the previous related works, the number of Eps and AM’s memory capacity are extensively increased. The simulation results are illustrated and some reliable associative memories examples are shown at the end of this paper.

Time delays play important roles in genetic regulatory networks. In this paper, a gene regulatory network model with time delays and mutual inhibition is considered, where time delays are regarded as bifurcation parameters. In the first part of this paper, we analyze the associated characteristic equations and obtain the conditions for the stability of the system and the existence of Hopf bifurcations in five special cases. Explicit formulas are given to determine the direction and stability of the Hopf bifurcation by using the normal form method and the center manifold theorem. Numerical simulations are then performed to illustrate the results we obtained. In the second part of the paper, using time-delayed stochastic numerical simulations, we study the impact of biological fluctuations on the system and observe that, in modest noise regimes, unexpectedly, noise acts to stabilize the otherwise destabilized oscillatory system.

Quantum Neural Networks (QNN) models have attracted great attention since it innovates a new neural computing manner based on quantum entanglement. However, the existing QNN models are mainly based on the real quantum operations, and the potential of quantum entanglement is not fully exploited. In this paper, we proposes a novel quantum neuron model called Complex Quantum Neuron (CQN) that realizes a deep quantum entanglement. Also, a novel hybrid networks model Complex Rotation Quantum Dynamic Neural Networks (CRQDNN) is proposed based on Complex Quantum Neuron (CQN). CRQDNN is a three layer model with both CQN and classical neurons. An infinite impulse response (IIR) filter is embedded in the Networks model to enable the memory function to process time series inputs. The Levenberg-Marquardt (LM) algorithm is used for fast parameter learning. The networks model is developed to conduct time series predictions. Two application studies are done in this paper, including the chaotic time series prediction and electronic remaining useful life (RUL) prediction. A novel hybrid networks model Complex Rotation Quantum Dynamic Neural Networks (CRQDNN) is proposed.Deep quantum entanglement is realized by incorporating Complex Quantum Neurons (QRN).The embedded IIR filter structure enables the dynamic properties to treat with time series input.The application studies of chaotic time series prediction and electronic prognostics are investigated.

This paper is concerned with the problem of coexistence and dynamical behaviors of multiple equilibrium points for neural networks with discontinuous non-monotonic piecewise linear activation functions and time-varying delays. The fixed point theorem and other analytical tools are used to develop certain sufficient conditions that ensure that the n -dimensional discontinuous neural networks with time-varying delays can have at least 5 n equilibrium points, 3 n of which are locally stable and the others are unstable. The importance of the derived results is that it reveals that the discontinuous neural networks can have greater storage capacity than the continuous ones. Moreover, different from the existing results on multistability of neural networks with discontinuous activation functions, the 3 n locally stable equilibrium points obtained in this paper are located in not only saturated regions, but also unsaturated regions, due to the non-monotonic structure of discontinuous activation functions. A numerical simulation study is conducted to illustrate and support the derived theoretical results. Discontinuous non-monotonic piecewise linear activation functions are introduced.Multiple equilibriums of neural networks with time-varying delays are investigated. n -dimensional discontinuous neural networks with delays can have 5 n equilibriums. 3 n equilibriums are locally stable and the others 5 n - 3 n are unstable.Discontinuous NNs can have greater storage capacity than continuous NNs.

This paper suggests a methodology for the identification, classification, and evaluation of various types of interactions that may occur in an HVDC link based on modular multi-level converters (MMC). The methodology incorporates the most suitable analytic tools for the frequency-domain study of each interaction category. To do so, a detailed nonlinear model of an MMC-based HVDC link that consists of master and slave MMCs, AC grids, and the DC transmission system is derived. Then, it is linearized to obtain a multi-input multi-output (MIMO) linear model that represents the dynamics of the complete MMC-based HVDC link. Based on the control loops of interest, interactions are classified as (1) state variable interactions, (2) disturbance interactions, (3) control loop interactions, and (4) overall system interactions. Then, through the application examples, the mentioned four categories of interactions are studied in frequency domain via the relevant analytic tools. The results obtained from the frequency-domain analysis are validated by time-domain simulation.

Memristors can be employed to mimic biological neural synapses or to describe electromagnetic induction effects. To exhibit the threshold effect of electromagnetic induction, this paper presents a threshold flux-controlled memristor and examines its frequency-dependent pinched hysteresis loops. Using an electromagnetic induction current generated by the threshold memristor to replace the external current in 2-D Hindmarsh-Rose (HR) neuron model, a 3-D memristive HR (mHR) neuron model with global hidden oscillations is established and the corresponding numerical simulations are performed. It is found that due to no equilibrium point, the obtained mHR neuron model always operates in hidden bursting firing patterns, including coexisting hidden bursting firing patterns with bistability also. In addition, the model exhibits complex dynamics of the actual neuron electrical activities, which acts like the 3-D HR neuron model, indicating its feasibility. In particular, by constructing the fold and Hopf bifurcation sets of the fast-scale subsystem, the bifurcation mechanisms of hidden bursting firings are expounded. Finally, circuit experiments on hardware breadboards are deployed and the captured results well match with the numerical results, validating the physical mechanism of biological neuron and the reliability of electronic neuron.

A network is scale-free if its connectivity density function is proportional to a power-law distribution. It has been suggested that scale-free networks may provide an explanation for the robustness observed in certain physical and biological phenomena, since the presence of a few highly connected hub nodes and a large number of small-degree nodes may provide alternate paths between any two nodes on average—such robustness has been suggested in studies of metabolic networks, gene interaction networks and protein folding. A theoretical justification for why many networks appear to be scale-free has been provided by Barabási and Albert, who argue that expanding networks, in which new nodes are preferentially attached to highly connected nodes, tend to be scale-free. In this paper, we provide the first efficient algorithm to compute the connectivity density function for the ensemble of all homopolymer secondary structures of a user-specified length—a highly nontrivial result, since the exponential size of such networks precludes their enumeration. Since existent power-law fitting software, such as , cannot be used to determine a power-law fit for our exponentially large RNA connectivity data, we also implement efficient code to compute the maximum likelihood estimate for the power-law scaling factor and associated Kolmogorov–Smirnov p value. Hypothesis tests strongly indicate that homopolymer RNA secondary structure networks are not scale-free; moreover, this appears to be the case for real (non-homopolymer) RNA networks.

This paper from new perspectives discusses the global synchronization of multiple recurrent neural networks (MNNs) with time delays via impulsive coupling. A new concept (coupling strength) is introduced, it is a variable parameter and plays a key role on synchronization. The selection of coupling strength can bring more convenience to the design of the impulsive coupling controller. Four results are presented for the synchronization of MNNs with time delays by using impulsive coupling with the coupling gain and variable topology, where two results are dependent on topology and other two results are independent on topological connectivity. In our results, the effects of each NN, coupling topology, and coupling strength can be positive or negative role on synchronization. In addition, three examples are presented to test our results in the theory analysis.

Implicit in the k–means algorithm is a way to assign a value, or utility, to a cluster of points. It works by taking the centroid of the points and the value of the cluster is the sum of distances from the centroid to each point in the cluster. The aim in this paper is to introduce an alternative way to assign a value to a cluster. Motivation is provided. Moreover, whereas the k–means algorithm does not have a natural way to determine k if it is unknown, we can use our method of evaluating a cluster to find good clusters in a sequential manner. The idea uses optimizations over permutations and clusters are set by the cyclic groups; generated by the Hungarian algorithm.

Entropy is an important index for describing the structure, function, and evolution of network. The existing research on entropy is primarily applied to undirected networks. Compared with an undirected network, a directed network involves a special asymmetric transfer. The research on the entropy of directed networks is very significant to effectively quantify the structural information of the whole network. Typical complex network models include nearest-neighbour coupling network, small-world network, scale-free network, and random network. These network models are abstracted as undirected graphs without considering the direction of node connection. For complex networks, modeling through the direction of network nodes is extremely challenging. In this paper, based on these typical models of complex network, a directed network model considering node connection in-direction is proposed, and the eigenvalue entropies of three matrices in the directed network is defined and studied, where the three matrices are adjacency matrix, in-degree Laplacian matrix and in-degree signless Laplacian matrix. The eigenvalue-based entropies of three matrices are calculated in directed nearest-neighbor coupling, directed small world, directed scale-free and directed random networks. Through the simulation experiment on the real directed network, the result shows that the eigenvalue entropy of the real directed network is between the eigenvalue entropy of directed scale-free network and directed small-world network.

This paper is concerned with the multistability of switched neural networks with piecewise linear activation functions under state-dependent switching. Under some reasonable assumptions on the switching threshold and activation functions, by using the state-space decomposition method, contraction mapping theorem, and strictly diagonally dominant matrix theory, we can characterize the number of equilibria as well as analyze the stability/instability of the equilibria. More interesting, we can find that the switching threshold plays an important role for stable equilibria in the unsaturation regions of activation functions, and the number of stable equilibria of an $n$ -neuron switched neural network with state-dependent parameters increases to $3^{n}$ from $2^{n}$ in the conventional one. Furthermore, for two-neuron switched neural networks, the precise attraction basin of each stable equilibrium point can be figured out, and its boundary is composed of the stable manifolds of unstable equilibrium points and the switching lines. Two simulation examples are discussed in detail to substantiate the effectiveness of the theoretical analysis.

In structured populations the spatial arrangement of cooperators and defectors on the interaction graph together with the structure of the graph itself determines the game dynamics and particularly whether or not fixation of cooperation (or defection) is favored. For networks described by regular graphs and for a single cooperator (and a single defector) the question of fixation can be addressed by a single parameter, the structure coefficient. This quantity is invariant with respect to the location of the cooperator on the graph and also does not vary over different networks. We may therefore consider it to be generic for regular graphs and call it the generic structure coefficient. For two and more cooperators (or several defectors) fixation properties can also be assigned by structure coefficients. These structure coefficients, however, depend on the arrangement of cooperators and defectors which we may interpret as a configuration of the game. Moreover, the coefficients are specific for a given interaction network modeled as a regular graph, which is why we may call them specific structure coefficients. In this paper, we study how specific structure coefficients vary over interaction graphs and analyze how spectral properties of interaction networks relate to specific structure coefficients. We also discuss implications for the benefit-to-cost ratios of donation games.

Membrane proteins are a major focus for new drug discovery. Transmembrane beta-barrel proteins play key roles in the translocation machinery, pore formation, membrane anchoring and ion exchange. Given their key roles and the difficulty in membrane protein structure determination, the use of computational modelling is essential. This paper focuses on the topology prediction of transmembrane beta-barrel proteins. In the field of bioinformatics, many years of research has been spent on the topology prediction of transmembrane alpha-helices. The efforts to TMB (transmembrane beta-barrel) proteins topology prediction have been overshadowed and the prediction accuracy could be improved with further research. Various methodologies have been developed in the past for the prediction of TMB proteins topology, however the use of cascading classifier has never been fully explored. This research presents a novel approach to TMB topology prediction with the use of a cascading classifier. The MATLAB computer simulation results show that the proposed methodology predicts transmembrane beta-barrel proteins topologies with high accuracy for randomly selected proteins. By using the cascading classifier approach the best overall accuracy is 76.3% with a precision of 0.831 and recall or probability of detection of 0.799 for TMB topology prediction. The accuracy of 76.3% is achieved using a two-layers cascading classifier.

Since the seminal 1961 paper of Monod and Jacob, mathematical models of biomolecular circuits have guided our understanding of cell regulation. Model-based exploration of the functional capabilities of any given circuit requires systematic mapping of multidimensional spaces of model parameters. Despite significant advances in computational dynamical systems approaches, this analysis remains a nontrivial task. Here, we use a nonlinear system of ordinary differential equations to model oocyte selection in Drosophila, a robust symmetry-breaking event that relies on autoregulatory localization of oocyte-specification factors. By applying an algorithmic approach that implements symbolic computation and topological methods, we enumerate all phase portraits of stable steady states in the limit when nonlinear regulatory interactions become discrete switches. Leveraging this initial exact partitioning and further using numerical exploration, we locate parameter regions that are dense in purely asymmetric steady states when the nonlinearities are not infinitely sharp, enabling systematic identification of parameter regions that correspond to robust oocyte selection. This framework can be generalized to map the full parameter spaces in a broad class of models involving biological switches., Author summary Identification of qualitatively different regimes in models of biomolecular switches is essential for understanding dynamics of complex biological processes, including symmetry breaking in cells and cell networks. We demonstrate how topological methods, symbolic computation, and numerical simulations can be combined for systematic mapping of symmetry-broken states in a mathematical model of oocyte specification in Drosophila, a leading experimental system of animal oogenesis. Our algorithmic framework reveals global connectedness of parameter domains corresponding to robust oocyte specification and enables systematic navigation through multidimensional parameter spaces in a large class of biomolecular switches.

The brain consists of many interconnected networks with time-varying, partially autonomous activity. There are multiple sources of noise and variation yet activity has to eventually converge to a stable, reproducible state (or sequence of states) for its computations to make sense. We approached this problem from a control-theory perspective by applying contraction analysis to recurrent neural networks. This allowed us to find mechanisms for achieving stability in multiple connected networks with biologically realistic dynamics, including synaptic plasticity and time-varying inputs. These mechanisms included inhibitory Hebbian plasticity, excitatory anti-Hebbian plasticity, synaptic sparsity and excitatory-inhibitory balance. Our findings shed light on how stable computations might be achieved despite biological complexity. Crucially, our analysis is not limited to analyzing the stability of fixed geometric objects in state space (e.g points, lines, planes), but rather the stability of state trajectories which may be complex and time-varying., Author summary Stability is essential for any complex system including, and perhaps especially, the brain. The brain’s neural networks are highly dynamic and noisy. Activity fluctuates from moment to moment and can be highly variable. Yet it is critical that these networks reach a consistent state (or sequence of states) for their computations to make sense. Failures in stability have consequences ranging from mild (e.g incorrect decisions) to severe (disease states). In this paper we use tools from control theory and dynamical systems theory to find mechanisms which produce stability in recurrent neural networks (RNNs). We show that a kind of “unlearning” (inhibitory Hebbian and excitatory anti-Hebbian plasticity), balance of excitation and inhibition, and sparse anatomical connectivity all lead to stability. Crucially, we focus on the stability of neural trajectories. This is different from traditional studies of stability of fixed points or planes. We do not assess what trajectories our networks will follow but, rather, when these trajectories will all converge towards each other to achieve stability.

Inspired by recent biological experiments, we simulate animals moving in different environments (open space, spiral mazes and on a treadmill) to test the performances of a simple model of the retrosplenial cortex (RSC) acting as a path integration (PI) and as a categorization mechanism. The connection between the hippocampus, RSC and the entorhinal cortex is revealed through a novel perspective. We suppose that the path integration is performed by the information coming from RSC. Grid cells in the entorhinal cortex then can be built as the result of a modulo projection of RSC activity. In our model, PI is performed by a 1D field of neurons acting as a simple low-pass filter of head direction (HD) cells modulated by the linear velocity of the animal. Our paper focuses on the constraints on the HD cells shape for a good approximation of PI. Recording of neurons on our 1D PI field shows these neurons would not be intuitively interpreted as performing PI. Using inputs coming from a narrow neighbouring projection of our PI field creates place cell-like activities in the RSC when the mouse runs on the treadmill. This can be the result of local self-organizing maps representing blobs of neurons in the RSC (e.g. cortical columns). Other simulations show that accessing the whole PI field would induce place cells whatever the environment is. Since this property is not observed, we conclude that the categorization neurons in the RSC should have access to only a small fraction of the PI field.

Network modeling is an effective tool for understanding the properties of complex biological systems. Networks are widely used to help us gain insight into biological systems. In this way, the cell, gene, and protein are denoted as nodes, and the connection elements are regarded as links or edges. In this paper, a novel stochastic strategy is developed for identifying the most influential edges on the stability of biological networks. Regarding the principles of networks and control-theory basics like Jacobian and eigenvalue sensitivity-based analysis, a new criterion is proposed, called “random sensitivity index matrix” (RSIM). RSIM evaluates the eigenvalue sensitivity of all edges in a network in the presents of stochastic disturbances based on the Monte Carlo algorithm. Through the values of RSIM elements, the sensitive edges are identifiable. In addition, the contribution of each edge in network instability has been compared through different percentages of disturbances. Different percentages of disturbances did not change the results. The performance of the proposed method was verified by simulation results for Lac (lactose) operon and MAPK (Mitogen-activated protein kinases) as two sample biological networks.

In certain swarm applications, where the inter-agent distance is not the only factor in the collective behaviours of the swarm, additional properties such as density could have a crucial effect. In this paper, we propose applying a Distance-Weighted K-Nearest Neighbouring (DW-KNN) topology to the behaviour of robot swarms performing self-organized aggregation, in combination with a virtual physics approach to keep the robots together. A distance-weighted function based on a Smoothed Particle Hydrodynamic (SPH) interpolation approach, which is used to evaluate the robot density in the swarm, is applied as the key factor for identifying the K-nearest neighbours taken into account when aggregating the robots. The intra virtual physical connectivity among these neighbours is achieved using a virtual viscoelastic-based proximity model. With the ARGoS based-simulator, we model and evaluate the proposed approach, showing various self-organized aggregations performed by a swarm of N foot-bot robots. Also, we compared the aggregation quality of DW-KNN aggregation approach to that of the conventional KNN approach and found better performance.

In this paper, we investigated the performance of a two-way satellite-terrestrial DF relay network with asymmetric simultaneous wireless information and power transfer (SWIPT). In particular, selective physical-layer network coding (SPNC) was employed in the proposed network, improving the throughput performance. We derived the expressions of system average end-to-end throughput and single node detection (SND) occurrence probability. Furthermore, to observe the effects of the power splitting (PS) coefficient on the energy efficiency performance, the expressions of energy harvested in the physical-layer network coding (PNC) and SPNC protocol were also derived. Finally, theoretical analyses and Monte Carlo simulation results are presented to show: (i) SPNC protocol outperforms the conventional PNC protocol in the two-way satellite-terrestrial relay network with SWIPT in infrequent light shadowing (ILS), average shadowing (AS), and frequent heavy shadowing (FHS) Shadowed-Rician fading channels; (ii) as the channel state gets worse, SPNC protocol can achieve more performance improvement than PNC protocol; (iii) as the PS coefficient increases, the average end-to-end throughput performance increases progressively, and the average energy efficiency performance increases progressively within a certain range, while decreasing in the others.

Removing influential nodes or shortcuts in a network restrains epidemic or information diffusion, but this method destroys the connectivity of the network and changes the topological structure. As an alternative, an additional field can be imposed in the network to affect node behaviors and slow down diffusion dynamics. However, little research has been performed systematically to analyze and compare these methods. This paper investigates epidemic dynamics and proposes the following four methods to restrain the diffusion process: blocking nodes, blocking edges, distracting node attention, and propagating opposite information. We compare differences in the actions of these methods, and investigate their joint effects. Through numerical experiments in a scale-free network and a real network, we observe that these methods change the spreading threshold and final extent with different conditions. The method of blocking nodes is more efficient and economical than blocking edges. Propagating opposite information can effectively prevent diffusion of target information that has a large spreading rate, whereas distracting node attention only takes effect for the information with a small rate. Meanwhile, the effects of these two methods mainly depend on their action time. From the joint effects, we can select the optimal method for different situations.

In this paper, finite-time synchronization (FTS) of memristor-based recurrent neural networks (MNNs) with time-varying delays is investigated by designing a new switching controller. First, by using the differential inclusions theory and set-valued maps, sufficient conditions to ensure FTS of MNNs are obtained under the two cases of 0

Information diffusion has been widely discussed in various disciplines including sociology, economics, physics or computer science. In this paper, we generalize the linear threshold model in signed networks consisting of both positive and negative links. We analyze the dynamics of the spread of information based on balance theory, and find that a signed network can generate path dependence while structural balance can help remove the path dependence when seeded with balanced initialized active nodes. Simulation shows that the diffusion of information based on positive links contradicts that based on negative links. More positive links in signed networks are more likely to activate nodes and remove path dependence, but they can reduce predictability that is based on active states. We also find that a balanced structure can facilitate both the magnitude and speed of information diffusion, remove the path dependence, and cause polarization.

This paper focuses on the exponential $ {\mathcal {H}}_ {\infty }$ filtering issue for a class of continuous-time switched neural networks (NNs). Our aim is to design a mode-dependent filter acquiring the state of the investigated system, and ensuring the global uniform exponential stability of the resulting filtering error system. The persistent dwell-time (PDT) switching strategy is employed to represent the switching among NNs. By utilizing a suitable Lyapunov function and the switched system theory, some criteria for the solvability of the addressed problem are presented under the full consideration of switching frequency. Finally, the filter gains are derived by a straightforward decoupling method, and with the aid of the algorithm of the continuous-time PDT switching regularity, the availability of the filter is expounded through a numerical example.

In this paper, we study targeted immunization in a multilayer Boolean network model for genetic regulatory networks. Given a specific set of nodes immune to perturbations, we find that the stability of a multilayer Boolean network is determined by the largest eigenvalue of the weighted non-backtracking matrix of corresponding aggregated network. Aimed to minimize this largest eigenvalue, we developed the metric of multilayer collective influence (MCI) to quantify the impact of immunizing individual nodes on the stability of the system. Compared with other competing heuristics, immunizing nodes with high MCI scores can stabilize an unstable multilayer network with higher efficiency on both synthetic and real-world networks. Moreover, despite that coupling nodes can exert direct influence across multiple layers, they are found to exhibit less importance as measured by the MCI score. Our work reveals the mechanism of maintaining the stability of multilayer Boolean networks and provides an efficient targeted immunization strategy, which can be potentially applied to the location of pathogenesis of diseases and the development of targeted therapy.

This paper presents the Hybrid Scalable-Minimized-Butterfly-Fat-Tree (H-SMBFT) topology for on-chip communication. Main aspects of this work are the description of the architectural design and the characteristics as well as a comparative analysis against two established indirect topologies namely Butterfly-Fat-Tree (BFT) and Scalable-Minimized-Butterfly-Fat-Tree (SMBFT). Simulation results demonstrate that the proposed topology outperforms its predecessors in terms of performance, area and power dissipation. Specifically, it improves the link interconnectivity between routing levels, such that the number of required links isreduced. This results into reduced router complexity and shortened routing paths between any pair of communicating nodes in the network. Moreover, simulation results under synthetic as well as real-world embedded applications workloads reveal that H-SMBFT can reduce the average latency by up-to35.63% and 17.36% compared to BFT and SMBFT, respectively. In addition, the power dissipation of the network can be reduced by up-to33.82% and 19.45%, while energy consumption can be improved byup-to32.91% and 16.83% compared to BFT and SMBFT, respectively.

The cross-section of a cell in a monolayer epithelial tissue can be modeled mathematically as a k-sided polygon. Empirically studied distributions of the proportions of k-sided cells in epithelia show remarkable similarities in a wide range of evolutionarily distant organisms. A variety of mathematical models have been proposed for explaining this phenomenon. The highly parsimonious simulation model of (Patel et al., PLoS Comput. Biol., 2009) that takes into account only the number of sides of a given cell and cell division already achieves a remarkably good fit with empirical distributions from Drosophila, Hydra, Xenopus, Cucumber, and Anagallis. Within the same modeling framework as in that paper, we introduce additional options for the choice of the endpoints of the cleavage plane that appear to be biologically more realistic. By taking the same data sets as our benchmarks, we found that combinations of some of our new options consistently gave better fits with each of these data sets than previously studied ones. Both our algorithm and simulation data are made available as research tools for future investigations.

Cluster synchronization is a typical collective behavior in coupled dynamical systems, where the synchronization occurs within one group, while there is no synchronization among different groups. In this paper, under event-based mechanism, pinning cluster synchronization in an array of coupled neural networks is studied. A new event-triggered sampled-data transmission strategy, where only local and event-triggering states are utilized to update the broadcasting state of each agent, is proposed to realize cluster synchronization of the coupled neural networks. Furthermore, a self-triggered pinning cluster synchronization algorithm is proposed, and a set of iterative procedures is given to compute the event-triggered time instants. Hence, this will reduce the computational load significantly. Finally, an example is given to demonstrate the effectiveness of the theoretical results.

In this paper, a learning algorithm is developed for Dynamic Plastic Continuous Neural Networks (DPCNNs) to improve their learning of highly nonlinear time dependent problems. A DPCNN is comprised of a base medium, which is nonlinear and plastic, and a number of neurons that are attached to the base by wire-like connections similar to perceptrons. The information is distributed within DPCNNs gradually and through wave propagation mechanism. While a DPCNN is adaptive due to its connection weights, the material properties of its base medium can also be adjusted to improve its learning. The material of the medium is plastic and can contribute to memorizing the history of input-response similar to neuroplasticity in natural brain. The results obtained from numerical simulation of DPCNNs have been encouraging. Nonlinear plastic finite element modeling has been used for numerical simulation of dynamic behavior and wave propagation in the medium. Two significant differences of DPCNNs with other types of neural networks are that: (1) there is a medium to which the neurons are attached where the medium can contribute to the learning, (2) the input layer is not made of nodes but it is an edge terminal which is capable of receiving a continuous function over the input edge, though it is discretized in the finite element model. A DPCNN is reduced to a perceptron if the medium is removed and the neurons are connected to each other only by wires. Continuity of the input lets the discretization of data take place intrinsically within the DPCNN instead of being applied by the user.

This paper studies the consensus problem of networks with time-varying topology. Event-triggered rules are employed in diffusion coupling terms to reduce the updating load of the coupled system. Two strategies are considered: event-triggered strategy, that each node observes the state information in an instantaneous way, to determine the next triggering event time, and self-triggered strategy, that each node only needs to observe the state information at the event time to predict the next triggering event time. In each strategy, two kinds of algorithms are considered: the pull-based algorithm, that the diffusion coupling term of every node is updated at the latest observations of the neighborhood at its triggered time, and push-based algorithm, the diffusion coupling term of every node uses the state information of its neighborhood at their latest triggered time. It is proved that if the coupling matrix across time intervals with length less than some given constant has spanning trees, then the proposed algorithms can realize consensus. Examples with numerical simulation are provided to show the effectiveness of the theoretical results.

In this paper, the complete synchronizations for asynchronous switched Boolean network with free Boolean sequence controllers and close-loop controllers are studied. First, the basic asynchronous switched Boolean network model is provided. With the method of semi-tensor product, the Boolean dynamics is translated into linear representation. Second, necessary and sufficient conditions for ASBN synchronization with free Boolean sequence control and close-loop control are derived, respectively. Third, some illustrative examples are provided to show the efficiency of the proposed methods.

In this paper, we investigate a new variant of spiking neural P systems (SNP systems, in short), called spiking neural P systems with multiple channels and polarizations (SNP-MCP systems, in short). The variant integrates two interesting features: multiple channel and polarization. Each neuron can use its multiple channels to connect one or more subsequent sets of neurons. Moreover, both polarizations and regular expressions are used in rules to control the spiking of neurons. The computational power of the variant is discussed. The Turing universality of the variant as number generating/accepting devices is proven, and then a small universal system with 150 neurons is constructed to compute any Turing computable function.

In this paper, we propose a connectivity-preserving flocking algorithm for multi-agent systems in which the neighbor set of each agent is determined by the hybrid metric-topological distance so that the interaction topology can be represented as the range-limited Delaunay graph, which combines the properties of the commonly used disk graph and Delaunay graph. As a result, the proposed flocking algorithm has the following advantages over the existing ones. First, range-limited Delaunay graph is sparser than the disk graph so that the information exchange among agents is reduced significantly. Second, some links irrelevant to the connectivity can be dynamically deleted during the evolution of the system. Thus, the proposed flocking algorithm is more flexible than existing algorithms, where links are not allowed to be disconnected once they are created. Finally, the multi-agent system spontaneously generates a regular quasi-lattice formation without imposing the constraint on the ratio of the sensing range of the agent to the desired distance between two adjacent agents. With the interaction topology induced by the hybrid distance, the proposed flocking algorithm can still be implemented in a distributed manner. We prove that the proposed flocking algorithm can steer the multi-agent system to a stable flocking motion, provided the initial interaction topology of multi-agent systems is connected and the hysteresis in link addition is smaller than a derived upper bound. The correctness and effectiveness of the proposed algorithm are verified by extensive numerical simulations, where the flocking algorithms based on the disk and Delaunay graph are compared.