Graphic Methods in Topological Dynamics

This paper considers the graph sequence graph （f^n ）={x×f^n ： x ∈X} of the iterates f^n of a continuous map f ： X →X on a compact metric space （X, d）. The main aim is to introduce serval limit sets by using different recurrent time sets, and discuss the relation between dynamics of the underlying compact system （X, f） and the structure of these limit sets, from a topological or fractal viewpoint.

Progress and realization platforms of dynamic topological photonics

Dynamic topological photonics is a novel research field, combining the time-domain optics and topological physics.In this review, the recent progress and realization platforms of dynamic topological photonics have been well introduced.The definition, measurement methods and the evolution process of the dynamic topological photonics are demonstrated to better understand the physical diagram. This review is meant to bring the readers a different perspective on topological photonics, grasp the advanced progress of dynamic topology, and inspire ideas about future prospects.

SOME PROBLEMS ON FRACTAL GEOMETRY AND TOPOLOGICAL DYNAMICAL SYSTEMS

This paper is a continuation of [14], some new problems on fractal geometry and topological dynamical systems have been posed.

Power Flow Response Based Dynamic Topology Optimization of Bi-material Plate Structures

Work on dynamic topology optimization of engineering structures for vibration suppression has mainly addressed the maximization of eigenfrequencies and gaps between consecutive eigenfrequencies of free vibration, minimization of the dynamic compliance subject to forced vibration, and minimization of the structural frequency response. A dynamic topology optimization method of bi-material plate structures is presented based on power flow analysis. Topology optimization problems formulated directly with the design objective of minimizing the power flow response are dealt with. In comparison to the displacement or velocity response, the power flow response takes not only the amplitude of force and velocity into account, but also the phase relationship of the two vector quantities. The complex expression of power flow response is derived based on time-harmonic external mechanical loading and Rayleigh damping. The mathematical formulation of topology optimization is established based on power flow response and bi-material solid isotropic material with penalization(SIMP) model. Computational optimization procedure is developed by using adjoint design sensitivity analysis and the method of moving asymptotes(MMA). Several numerical examples are presented for bi-material plate structures with different loading frequencies, which verify the feasibility and effectiveness of this method. Additionally, optimum results between topological design of minimum power flow response and minimum dynamic compliance are compared, showing that the present method has strong adaptability for structural dynamic topology optimization problems. The proposed research provides a more accurate and effective approach for dynamic topology optimization of vibrating structures.

Multi-constraint quality of service routing algorithm for dynamic topology networks

An adaptive multi-QoS routing algorithm called AMQRA is proposed for dynamic topology networks, such as satellite networks and Ad-hoc networks. The AMQRA is a distributed and mobile-agents-based routing algorithm, which combines ant quantity system （AQS） with ant colony optimization （ACO） that is used in AntNet routing algorithm. In dynamic topology networks, the AMQRA achieves timely optimization for concave metric QoS constraint and fast convergence. The proposed routing algorithm is simulated in Iridium satellite constellation on OPNET. The results show that AMQRA not only outperforms the AntNet in convergence rate in dynamic topology networks but also can optimize concave metric QoS constraint and reasonably allot bandwidth to the load to avoid networks congestion.

Consensus of high-order continuous-time multi-agent systems with time-delays and switching topologies

Consensus problems of high-order continuous-time multi-agent systems with time-delays and switching topologies are studied. The motivation of this work is to extend second-order continuous-time multi-agent systems from the liter- ature. It is shown that consensus can be reached with arbitrarily bounded time-delays even though the communication topology might not have spanning trees. A numerical example is included to show the theoretical results.

An improved genetic algorithm with dynamic topology

The genetic algorithm （GA） is a nature-inspired evolutionary algorithm to find optima in search space via the interac- tion of individuals. Recently, researchers demonstrated that the interaction topology plays an important role in information exchange among individuals of evolutionary algorithm. In this paper, we investigate the effect of different network topolo- gies adopted to represent the interaction structures. It is found that GA with a high-density topology ends up more likely with an unsatisfactory solution, contrarily, a low-density topology can impede convergence. Consequently, we propose an improved GA with dynamic topology, named DT-GA, in which the topology structure varies dynamically along with the fitness evolution. Several experiments executed with 15 well-known test functions have illustrated that DT-GA outperforms other test GAs for making a balance of convergence speed and optimum quality. Our work may have implications in the combination of complex networks and computational intelligence.

Disagreement and Antagonism in Signed Networks: A Survey

Signed networks refer to a class of network systems including not only cooperative but also antagonistic interactions among nodes.Due to the existence of antagonistic interactions in signed networks,the agreement of nodes may not be established,instead of which disagreement behaviors generally emerge.This paper reviews several different disagreement behaviors in signed networks under the single-integrator linear dynamics,where two classes of topologies,namely,the static topology and the dynamic topology,are considered.For the static signed networks with the adjacency weights as(time-varying)scalars,we investigate the convergence behaviors and the fluctuation behaviors with respect to fixed topologies and switching topologies,respectively,and give some brief introductions on the disagreement behaviors of general time-varying signed networks.Correspondingly,several classes of behavior analysis approaches are also provided.For the dynamic signed networks with the adjacency weights as transfer functions or linear time-invariant systems,we show the specific descriptions and characteristics of them such that the disagreement behaviors can be obtained by resorting to the derived static signed graphs.Furthermore,we give their applications to the behavior analysis of static signed networks in the presence of high-order dynamics or communication delays.

Spreading behavior of SIS epidemic model on networks with dynamical topology

Based on the two-dimensional regular lattice,a modified SIS(Susceptible-Infected-Susceptible)epidemic model with motion rules is presented to study the spreading behavior on networks with dynamical topology.The mean-field theory is utilized to analyze the critical threshold(λc)of epidemic spreading under the randomly mixing conditions.It is found that λc is only related with the population density within the lattice.Large-scale numerical simulations are carried out to verify the mean-field results,and it is observed that the long-range probability p largely affects the epidemic spreading behavior.In addition,the effect of the dual time scales on epidemic spreading is also investigated by the simulations,and it is shown that the dual time scales accelerate the dynamic spreading behavior.The results indicate that the model with motion can help us to further understand the real epidemics.

Plotinus:A Satellite Internet Digital Twin System

The development of space-air-ground integrated networks (SAGIN) requires sophisticated satellite Internet emulation tools that can handle complex, dynamic topologies and offer in-depth analysis. Existing emulation platforms struggle with challenges like the need for detailed implementation across all network layers, real-time response, and scalability. This paper proposes a digital twin system based on microservices for satellite Internet emulation,namely Plotinus,which aims to solve these problems. Plotinus features a modular design, allowing for easy replacement of the physical layer to emulate different aerial vehicles and analyze channel interference. It also enables replacing of path computation methods to simplify testing and deploying algorithms. In particular, Plotinus allows for real-time emulation with live network traffic,enhancing practical network models. The evaluation result shows Plotinus’s effective emulation of dynamic satellite networks with real-world devices. Its adaptability for various communication models and algorithm testing highlights Plotinus’s role as a vital tool for developing and analyzing SAGIN systems, offering a cross-layer,real-time,and scalable digital twin system.

Probing the fractional topological charge of a vortex light beam by using dynamic angular double slits

Vortex beams with fractional topological charge(FTC) have many special characteristics and novel applications.However, one of the obstacles for their application is the difficulty of precisely determining the FTC of fractional vortex beams. We find that when a vortex beam with an FTC illuminates a dynamic angular double slit(ADS), the far-field interference patterns that include the information of the FTC of the beam at the angular bisector direction of the ADS vary periodically. Based on this property, a simple dynamic ADS device and data fitting method can be used to precisely measure the FTC of a vortex light beam with an error of less than 5%.

Optimization of a Network Topology Generation Algorithm Based on Spatial Information Network

Spatial information network(SIN)is a network with high speed and periodicity of node operation.In recent days,China will build a complete asteroid monitoring and warning system and a near-Earth asteroid defense system.This requires launching more low-Earth orbit satellites.In order to adapt to the increase in the number of near-Earth satellites,the dynamic optimization of space informa-tion network topology between satellites will have research significance.Consid-ering the visibility of satellite networking,the connectivity of satellite nodes,and the number of links connected to the whole network,with the goal of minimizing the end-to-end delay between satellite nodes in the network as the optimization goal,a network topology optimization model that meets multiple constraints is constructed,and the model is solved using greedy algorithm and simulated anneal-ing algorithm.In the process of simulated annealing,the networkflow algorithm is innovatively proposed for neighborhood solution.Experiments show that the simulated annealing hybrid neighborhood algorithm is significantly better than the simulated annealing random neighborhood algorithm.

Univoque graphs for non-integer base expansions

Unique expansions in non-integer bases have been investigated in many papers during the last thirty years.They are often conveniently generated by labeled directed graphs.We give a precise description of the set of sequences generated by these graphs.This provides a geometric explanation of many former abstract results in this domain.Our results are illustrated by many examples.

Topology tracking of dynamic UAV wireless networks

Wireless network is the communication foundation that supports the intelligentization of Unmanned Aerial Vehicle(UAV) swarm. The topology of UAV communication network is the key to understanding and analyzing the behavior of UAV swarm, thus supporting the further prediction of UAV operations. However, the UAV swarm network topology varies over time due to the high mobility and diversified mission requirements of UAVs. Therefore, it is important but challenging to research dynamic topology inference for tracking the topology changes of the UAV network,especially in non-cooperative manner. In this paper, we study the problem of inferring UAV swarm network topology based on external observations, and propose a dynamic topology inference method. First, we establish a sensing framework for acquiring the communication behavior of the target network over time. Then, we expand the multi-dimensional dynamic Hawkes process to model the communication event sequence in a dynamic wireless network. Finally, combining the sliding time window mechanism, the maximum weighted likelihood estimation is applied to inferring the network topology. Extensive simulation results demonstrate the effectiveness of the proposed method.

Dynamic survivable mapping through reconfiguration in IP over WDM network

A new approach for network survivability problem in Intemet protocol （IP） over wavelength division multiplexing （WDM） optical network is proposed to enhance the IP layer restorability under physical link failure through logical topology reconfiguration. More specifically, after traffic arrival and departure, reconfiguring the logical topology correspondingly is helpful to minimize the traffic disruption after physical link failure. So, in this paper, this problem is proposed for first time and formulated as an integer linear programming （ILP） problem. And then, two heuristic algorithms are proposed. The performance of proposed algorithms have been evaluated through simulations, and the results show that reconfiguring the logical topology dynamically could achieve more than 20% improvement of the restorability of traffic in IP layer, but with acceptable resource cost.

Bi-material Topology Optimization Using Analysis Mesh-Independent Point-Wise Density Interpolation

This paper extends the independent point-wise density interpolation to the bimaterial to pology optimization to improve the structural static or dynamic proper ties.In contras t to the conventional elemental density-based topology optimization approaches,this method employs an analysis-mesh-separated material density field discretization model to describe the topology evolution of bi-material structures within the design domain.To be specific,the density design variable points can be freely positioned,independently of the field points used for discretization of the displacement field.By this means,a material interface description of relatively high quality can be achieved,even when unstructured finite element meshes and irregular-shaped elements are used in discretization of the analysis domain.Numerical examples,regarding the minimum static compliance design and the maximum fundamental eigen-frequency design,are presented to demonstrate the validity and applicability of the proposed formulation and numerical techniques.It is shown that this method is free of numerical difficulties such as checkerboard patterns and the“islanding”phenomenon.

MULTI-AGENT AGGREGATION BEHAVIOR ANALYSIS: THE DYNAMIC COMMUNICATION TOPOLOGY

The authors extend the Gazi＇s swarm model with local neighbor rules and the dynamic communication topology, and study its aggregation properties. Results of analysis show that all agents in the models aggregate and eventually form a cohesive cluster of finite size around the swarm center or the appointed point. Finally, simulations are provided to testify some of the results. Models in the paper are more applicable to the reality for the advantage that each agent only needs the partial information of the entire dynamic system when making motion decision.

Impact of Wavelength-Routed Network Physical Topology on Blocking Probability Using a Dynamic Traffic Growth Model

We investigate the impact of network topology on blocking probability in wavelength-routed networks using a dynamic traffic growth model. The dependence of blocking on different physical parameters is assessed.