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We reinvestigate the dynamical behavior of a first order scalar nonlinear delay differential equation with piecewise linearity and identify several interesting features in the nature of bifurcations and chaos associated with it as a…
Traffic forecasting problem remains a challenging task in the intelligent transportation system due to its spatio-temporal complexity. Although temporal dependency has been well studied and discussed, spatial dependency is relatively less…
In real-world systems, the relationships and connections between components are highly complex. Real systems are often described as networks, where nodes represent objects in the system and edges represent relationships or connections…
A new approach is proposed to the integrated analysis of the time structure of synchronization of multidimensional chaotic systems. The method allows one to diagnose and quantitatively evaluate the intermittency characteristics during…
The interest in deep learning methods for solving traditional signal processing tasks has been steadily growing in the last years. Time delay estimation (TDE) in adverse scenarios is a challenging problem, where classical approaches based…
Time-delay systems are an important class of dynamical systems which provide a solid mathematical framework to deal with many application domains of interest ranging from biology, chemical, electrical, and mechanical engineering, to…
Recently, several complex network approaches to time series analysis have been developed and applied to study a wide range of model systems as well as real-world data, e.g., geophysical or financial time series. Among these techniques,…
This work concerns the dynamics of a certain class of delay differential equations (DDEs) which we refer to as state dependent delay maps. These maps are generated by delay differential equations where the derivative of the current state…
We study the synchronization of a linear array of globally coupled identical logistic maps. We consider a time-delayed coupling that takes into account the finite velocity of propagation of the interactions. We find globally synchronized…
In the study of dynamical systems on networks/graphs, a key theme is how the network topology influences stability for steady states or synchronized states. Ideally, one would like to derive conditions for stability or instability that…
Real-world dynamical systems with retardation effects are described in general not by a single, precisely defined time delay, but by a range of delay times. An exact mapping onto a set of $N+1$ ordinary differential equations exists when…
This paper presents a novel methodology for evaluating the boundedness, stability, and instability of some vector nonlinear systems with multiple time-varying delays and variable coefficients. The proposed technique develops two scalar…
Meeting the diverse delay requirements of emerging wireless applications is one of the most critical goals for the design of ultradense networks. Though the delay of point-to-point communications has been well investigated using classical…
We study the dynamics of networks with coupling delay, from which the connectivity changes over time. The synchronization properties are shown to depend on the interplay of three time scales: the internal time scale of the dynamics, the…
This paper investigates the global stability and the global asymptotic stability independent of the sizes of the delays of linear time-varying Caputo fractional dynamic systems of real fractional order possessing internal point delays. The…
Identifying the qualitative changes in time-series data provides insights into the dynamics associated with such data. Such qualitative changes can be detected through topological approaches, which first embed the data into a…
This paper revisits a recently developed methodology based on the matrix Lambert W function for the stability analysis of linear time invariant, time delay systems. By studying a particular, yet common, second order system, we show that in…
We consider both leaderless and leader-follower, possibly nonlinear, networks affected by time-varying communication delays. For such systems, we give a set of sufficient conditions that guarantee the convergence of the network towards some…
A general method for constructing simplicial complex from observed time series of dynamical systems based on the delay coordinate reconstruction procedure is presented. The obtained simplicial complex preserves all pertinent topological…
The richness of many complex systems stems from the interactions among their components. The higher-order nature of these interactions, involving many units at once, and their temporal dynamics constitute crucial properties that shape the…