Related papers: Organization and clasification of trajectories in …
Proposed to study the dynamics of physiological systems in which the evolution depends on the state in a previous time, the Mackey-Glass model exhibits a rich variety of behaviors including periodic or chaotic solutions in vast regions of…
The celebrated Mackey-Glass model describes the dynamics of physiological \textit{delayed} systems in which the actual evolution depends on the values of the variables at some \textit{previous} times. This kind of systems are usually…
The Mackey--Glass equation, which was proposed to illustrate nonlinear phenomena in physiological control systems, is a classical example of a simple looking time delay system with very complicated behavior. Here we use a novel approach for…
High-dimensional chaos displayed by multi-component systems with a single time-delayed feedback is shown to be accessible to time series analysis of a scalar variable only. The mapping of the original dynamics onto scalar time-delay systems…
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…
Equations of motion with delays naturally emerge in the analysis of complex biological control systems which are organized around biochemically mediated feedback interactions. We study the properties of a Mackey-Glass-type nonlinear map…
We report the identification of global phase synchronization (GPS) in a linear array of unidirectionally coupled Mackey-Glass time-delay systems exhibiting highly non-phase-coherent chaotic attractors with complex topological structure. In…
We consider a network of delay dynamical systems connected in a ring via unidirectional positive feedback with constant delay in coupling. For the specific case of Mackey-Glass systems on the ring topology, we capture the phenomena of…
Investigating the network stability or synchronization dynamics of multi-agent systems with time delays is of significant importance in numerous real-world applications. Such investigations often rely on solving the transcendental…
We study the mean-field phase diagram of glassy systems in a field pointing in the direction of a metastable state. We find competition among a ``magnetized'' and a ``disordered'' phase, that are separated by a coexistence line as in…
We introduce the map representation of a time-delayed system in the presence of delay time modulation. Based on this representation, we find the method by which to analyze the stability of that kind of a system. We apply this method to a…
Delayed processes are ubiquitous throughout biology. These delays may arise through maturation processes or as the result of complex multi-step networks, and mathematical models with distributed delays are increasingly used to capture the…
We investigate synchronization between two unidirectionally linearly coupled chaotic non-identical time-delayed systems and show that parameter mismatches are of crucial importance to achieve synchronization. We establish that independent…
We study the phase diagram of glassy systems in presence of an attractive coupling among real replicas. We find competition among a localized and a delocalized phase, that are separated by a coexistence line as in ordinary first order phase…
Time delays are a common perturbation in systems with many states, such as networked, distributed, or decentralized systems. Current methods analyzing the stability of large systems with time delay typically produce very conservative…
Delayed interactions are a common property of coupled natural systems and therefore arise in a variety of different applications. For instance, signals in neural or laser networks propagate at finite speed giving rise to delayed…
We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial…
For the first time, using a modified Ikeda model it is demonstrated analytically that anticipating synchronization can be obtained in chaotic time-delay systems governed by two characteristic delay times. We derive existence and stability…
We present an algorithm for the rigorous integration of Delay Differential Equations (DDEs) of the form $x'(t)=f(x(t-\tau),x(t))$. As an application, we give a computer assisted proof of the existence of two attracting periodic orbits…
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…