Dynamic Behavior Of Neural Networks Research Articles

Memristive Hopfield neural network with multiple controllable nonlinear offset behaviors and its medical encryption application

Memristors possess inherent nonlinearity and synaptic attributes, rendering them more suited for integration as synapses within neural networks compared to resistors. Furthermore, their utilization induces significant alterations in the dynamic behavior of neural networks, hence bestowing considerable value in the realm of secure communication applications. In this paper, an improved cosine memristor is proposed, three representative memristor Hopfield neural networks (MHNNs) are constructed using it as synapse. The MHNNs exhibit rich initial offset boost behaviors, we summarize these phenomena into four types based on the offset characteristics. In particular, these offset types can be converted by adjusting internal parameters of the memristor. In addition, the MHNNs are constructed and tested using both software and hardware components, validating the accuracy of theoretical simulation and the implementation of systems. Ultimately, a set of bit-plane level medical image encryption algorithm is proposed on the basis of MHNNs, which has excellent encryption performance and can effectively protect the privacy of patients.

Tree-structured neural networks: Spatiotemporal dynamics and optimal control

How the network topology drives the response dynamic is a basic question that has not yet been fully answered in neural networks. Elucidating the internal relation between topological structures and dynamics is instrumental in our understanding of brain function. Recent studies have revealed that the ring structure and star structure have a great influence on the dynamical behavior of neural networks. In order to further explore the role of topological structures in the response dynamic, we construct a new tree structure that differs from the ring structure and star structure of traditional neural networks. Considering the diffusion effect, we propose a diffusion neural network model with binary tree structure and multiple delays. How to design control strategies to optimize brain function has also been an open question. Thus, we put forward a novel full-dimensional nonlinear state feedback control strategy to optimize relevant neurodynamics. Some conditions about the local stability and Hopf bifurcation are obtained, and it is proved that the Turing instability does not occur. Moreover, for the formation of the spatially homogeneous periodic solution, some diffusion conditions are also fused together. Finally, several numerical examples are carried out to illustrate the results’ correctness. Meanwhile, some comparative experiments are rendered to reveal the effectiveness of the proposed control strategy.

Chimera States mediated by nonlocally attractive-repulsive coupling in FitzHugh–Nagumo neural networks

The spontaneous occurrence of heterogeneous behaviors in homogeneous systems is an intriguing phenomenon. Recently, a remarkable heterogeneous behavior, called “chimera states”, which consists of spatially coherent and incoherent domains, has been studied in a great variety of systems including physical, chemical, biological, or optical. In this paper, chimera states in FitzHugh–Nagumo (FHN) neural networks are investigated. The identical FHN neurons are assigned in a ring and nonlocally coupled by attractive and repulsive couplings. We show that, the chimera states can be induced by the cooperation of nonlocally attractive and repulsive interactions between these neurons. Moreover, depending on the strength and range of attractive or repulsive couplings, the neural networks display different spatiotemporal behaviors, including chimera states, multi-cluster (MC) chimera states, traveling waves, traveling coherent states, solitary states, bursting synchronizations, and synchronizations. These results suggest that attractive and repulsive couplings may play a crucial role in mediating dynamic behavior of neural networks, and these results could be useful in understanding and predicting the rich dynamics of neural networks.

Synchronous Dynamics in Multilayer Memristive Neural Networks: Effect of Electromagnetic Induction

Brain has a hierarchical structure with multiple connection types. To further explore the effect of electromagnetic induction on biological neural networks, in this paper, a two-layer small-world neuronal network with electrical intra-layer connections and memristive inter-layer connections was constructed. In specially, the two layer have different spiking and bursting activities. Electrical coupling strength and electromagnetic induction coefficient are taken as control parameter. Numerical results indicate that the two-layer neurons in different discharge states can achieve synchronization and the firing patterns of the synchronized neurons are related to the electromagnetic induction. Moreover, some particular dynamical states including chimera state and bursting transition are observed in the network. Then, the mechanisms of the two burst transitions are clarified. In addition, the statistical synchronization factor and average error are introduced to measure the intra-layer and inter-layer synchronization, respectively, which reveal that electrical coupling induces and enhances the synchronization more effectively for a higher electromagnetic induction coefficient. Our obtained results indicate that the electromagnetic induction exerts significant impact in modulating the dynamic behavior of neural networks, and provide a useful guidance on the study of physiological functions related to synchronization in the brain.

Chimera states and synchronization behavior in multilayer memristive neural networks

To study the effect of electromagnetic induction on the spatiotemporal dynamic behavior of neural networks, in this paper, we have mainly studied both the synchronization behavior and the evolution of chimera states (CS) in coupled neural networks. To do this, a multilayer memristive neural network was constructed by selecting the Hindmarsh–Rose neurons as the network nodes, and the effect of electromagnetic induction is introduced by using the cubic flux-controlled memristive model as synapse. For simplicity, the following coupling scheme is adopted: only the coupling connections for the neurons between different layers are considered with memristive synapses, while those neurons in each layer are still bidirectional coupled with the classical electrical synapses. It is found that, by adjusting the coupled strength of electrical synapses and the parameters of memristive synapses, the coexistence behavior of coherent and incoherent states, i.e., the CS, could appear in each layer. It is interesting that the CS are also found in inter-layer memristive synapse network. Furthermore, we have discussed the synchronization behavior in this multilayer memristive neural network, one can find when the whole multilayer network is in a synchronization state, not only the spatiotemporal consistency of the CS in each layer neural networks is observed, but also the memductance of all memristive synapses is completely synchronized. Our results suggest that the electromagnetic induction may play an important role in regulating the dynamic behavior of neural networks, and the introduction of memristive synapse into the biological neural network will provide useful clues for revealing the memory behavior of the neural system in human brain.

Complex dynamical behavior of neural networks in circuit implementation

Neural networks have abundant dynamic behaviors in nonlinear fields. In this paper, several circuit units are combined to realize some neuron-network models. The results of circuit simulation described by Multisim software demonstrates complex dynamical behaviors. It is shown that the phenomenon such as hyperchaos, limit cycles, homoclinic orbits of the designed circuits are closely similar to the results of numerical experiments.

Dynamical Behavior of Neural Networks with Anti-Symmetrical Cyclic Connections

We show that a unit-group, which represents a group of contiguous units with the same sign of output, is a dominant component for the dynamical behavior of a neural network with anti-symmetrical cyclic connections for the nearest neighbor connections and global connections. In transient state, it is shown that the unit-group has the dynamics such that the amount n of units which belong to the unit-group increases with time, and that the increasing rate of n decreases with increasing n. The dynamics cause the large difference of the number of limit-cycles between discrete and continuous time models. Additionally, the period of the limit-cycle depends on the size of the unit-groups. This dependency is obtained from computer simulations and two approximation methods. These approximations provide the lower and the upper bounds of the periods which depend on the gain of an activation function. Using these approximations, we also obtain detailed relations between a period and the other network parameters analytically.

Algebraic decay of correlations in neural networks.

Dynamic behavior of neural networks is studied via the dynamic mean-field theory for the Little-Hopfield model and for the dynamic model. In both models, the existence of the generalized Almeida-Thouless lines and associated dynamic instabilities are revealed. On these lines, autocorrelation functions are found to decay algebraically with exponent 1/2, while they decay exponentially above the lines

Exponential stability and trajectory bounds of neural networks under structural variations

The dynamic behavior of neural networks under arbitrary unknown structural perturbations depends essentially on the compatibility/incompatibility of input variables in these networks. Estimates of the upper bounds of the motions of neural networks of either type and exponential stability of compatible neural networks are established by using three different forms of Lyapunov functions. Conditions for the maximum possible estimate of the domain of structural exponential stability are determined. All new concepts such as compatible/incompatible neural networks and structural exponential stability are defined. All the conditions are stated in simple algebraic forms. Their applications are straightforward. >

Projection method formulations of Hopfield-type associative memory neural networks

We study certain neural network architectures, which admit to optical implementations, from the point of view of projection methods. This approach enables us to uncover some interesting facts about the stable states of such networks. For example, a Hopfield-type associative content-addressable memory (ACAM) using a hard-limiter nonlinearity has three kinds of possible stable states. If the hard-limiter is replaced by a unity-slope saturation nonlinearity, there are only two kinds of stable states. These and other results demonstrate the utility of using projection methods in analyzing the dynamic behavior of neural networks.

Dynamic Behavior c with Chemical Markers

Abstract In this paper we studied the dynamic behavior of neural networks consisting of discrete populations of formal neurons. Neurons are assumed to have the same probability of connection with other neurons carrying the same type of chemical marker and divided in such a way to neural subpopulations due to the chemical affinity of markers carried by the individual cells. The dynamics of isolated networks as well as the ones that receive sustained external inputs show multiple stability and hysteresis phenomena which lead to multiple memory domains.