How to recover the underlying connection topology of a complex network from observed time series of a component variable of each node subject to random perturbations is studied. A new technique termed Piecewise Granger Causality is proposed. The validity of the new approach is illustrated with two FitzHugh-Nagumo neurobiological networks by only observing the membrane potential of each neuron, where the neurons are coupled linearly and nonlinearly, respectively. Comparison with the traditional Granger causality test is performed, and it is found that the new approach outperforms the traditional one. The impact of the network coupling strength and the noise intensity, as well as the data length of each partition of the time series, is further analyzed in detail. Finally, an application to a network composed of coupled chaotic Rössler systems is provided for further validation of the new method.
This article highlights particular mixed-mode oscillations (MMO) based on canard explosion observed in a fractional-order Fitzhugh-Nagumo (FFHN) model. In order to rigorously analyze the dynamics of the FFHN model, a recently introduced mathematical notion, the Hopf-like bifurcation (HLB), which provides a precise definition for the change between a fixed point and an S −asymptotically T −periodic solution, is used. The existence of HLB in this FFHN model is proved and the appearance of MMO based on canard explosion in the neighborhoods of such HLB points are numerically investigated using a new algorithm: the global-local canard explosion search algorithm. This MMO is constituted of various patterns of solutions with an increasing number of small-amplitude oscillations when two key parameters of the FFHN model are varied simultaneously. On the basis of such numerical experiment, it is conjectured that chaos could occur in a two-dimensional fractional-order autonomous dynamical system, with the fractional-order close to one. Therefore, this very simple two-dimensional FFHN model, presents an incredible ability to mimic the complex dynamics of neurons.
This paper introduces a novel complex network model to evaluate the reputation of virtual organizations. By using the Lyapunov function and linear matrix inequality approaches, the local synchronization of the proposed model is further investigated. Here, the local synchronization is defined by the inner synchronization within a group which does not mean the synchronization between different groups. Moreover, several sufficient conditions are derived to ensure the local synchronization of the proposed network model. Finally, several representative examples are given to show the effectiveness of the proposed methods and theories.
In this paper, a systematic design approach based on time-delay feedback is developed for chaotification of a continuous-time, feedback linearizable system. The chaotification is accomplished based on nonlinear control theory and an approximate relationship between a time-delay differential equation and a discrete map. An example is given to illustrate the systematic design procedure.
This paper formulates and studies a model of periodic delayed neural networks. This model can well describe many practical architectures of delayed neural networks, which is generalization of some additive delayed neural networks such as delayed Hopfied neural networks and delayed cellular neural networks, under a time-varying environment, particularly when the network parameters and input stimuli are varied periodically with time. Without assuming the smoothness, monotonicity and boundedness of the activation functions, the two functional issues on neuronal dynamics of this periodic networks, i.e. the existence and global exponential stability of its periodic solutions, are investigated. Some explicit and conclusive results are established, which are natural extension and generalization of the corresponding results existing in the literature. Furthermore, some examples and simulations are presented to illustrate the practical nature of the new results.
Under three necessary conditions for preserving the essential qualitative properties of the 3D Lorenz system, a general 2D quadratic autonomous system is converted to a 2D Lorenz-type system (2DLTS). A canonical form of the 2DLTS is derived with aid of a normalization technique. It is found that the 2DLTS can be converted to the 2D Duffing oscillator model under certain conditions. Furthermore, it is shown that the 2DLTS undergoes pitchfork bifurcation and Hopf bifurcation. Finally, approximate periodic solutions of both the 2DLTS near the Hopf bifurcation point and a time-periodically forced system are obtained.
No abstract is provided for this article.
Generalized Fock (GF) spaces were introduced by de Figueiredo and associates in late 1970's and early 1980's for generic representation of the input-output maps of nonlinear dynamical systems. Since then the underlying concepts and methods have been used and further developed by the present authors and others in the context of a number of applications including neural networks (see, e.g., the paper by de Figueiredo in the invited session on Fundamental of Neural Networks in this ISCAS'96 Proceedings). A GF Space F consists of sequences of tensor products of a given Hilbert space H. When H is L/sub 2/(R), the elements of F are Volterra series. In the present paper we introduce a GF space F whose elements are constructed from an L/sub 2/(R) equipped with an orthonormal wavelet basis. This provides a unique setting for modeling identification and control of nonlinear dynamical systems at multiple scales as elicited by the underlying wavelet basis.
Resource competition and intentional disruptions, grounded in rational intergroup conflict theory, play a central role in driving strategic rivalry in networked games. These mechanisms mirror real-world conflict dynamics, profoundly shaping decision-making processes and interfering with systemic stability. This study investigates the modeling and dynamics of networked evolutionary games with intergroup conflict (NEGs-IC). In the proposed framework, players are assigned a finite number of health points, which decrease when attacked–affecting both survivability and strategic interactions. Leveraging logical dynamical system modeling, we capture the co-evolution of strategies, payoffs, health points, and player actions, demonstrating that NEGs-IC can be effectively represented as a logical dynamic system. To characterize collective interest in NEGs-IC, we introduce an objective function that balances group cooperation and health point attrition. Based on this formulation, we define three evaluation criteria–optimal, suboptimal, and weak–to assess collective interest. An illustrative example is also presented to analyze network-based conflicts, offering insights into strategic behavior in adversarial environments.
Remote Direct Memory Access (RDMA) has been haunted by the need of pinning down memory regions. Pinning limits the memory utilization because it impedes on-demand paging and swapping. It also increases the initialization latency of large memory applications from seconds to minutes. To remove memory pining, existing approaches often require special hardware which supports page fault, and still have inferior performance. We propose NP-RDMA, which removes memory pinning during memory registration and enables dynamic page fault handling with commodity RDMA NICs. NP-RDMA does not require NICs to support page fault. Instead, by monitoring local memory paging and swapping with MMU-notifier, combining with IOMMU/SMMU-based address mapping, NP-RDMA efficiently detects and handles page fault in the software with near-zero additional latency to non-page-fault RDMA verbs. We implement an LD_PRELOAD library (with a modified kernel module), which is fully compatible with existing RDMA applications. Experiments show that NP-RDMA adds only 0.1{\sim}2 {\mu}s latency under non-page-fault scenarios. Moreover, NP-RDMA adds only 3.5{\sim}5.7 {\mu}s and 60 {\mu}s under minor or major page faults, respectively, which is 500x faster than ODP which uses advanced NICs that support page fault. With non-pinned memory, Spark initialization is 20x faster and the physical memory usage reduces by 86% with only 5.4% slowdown. Enterprise storage can expand to 5x capacity with SSDs while the average latency is only 10% higher. To the best of our knowledge, NP-RDMA is the first efficient and application-transparent software approach to remove memory pinning using commodity RDMA NICs.
We study the problem of existence of homoclinic and heteroclinic orbits of Chen's system. For the case of 2c > a > c > 0 and b ≥ 2a, we prove that the system has no homoclinic orbit but has two and only two heteroclinic orbits.
