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Biological systems operate under persistent noise, which can alter system states and induce transitions between attractors. Here, we study the attractor dynamics of Boolean networks focusing on the transitions between attractors induced by…
For systems with hidden attractors and unstable equilibria, the property that hidden attractors are not connected with unstable equilibria is now accepted as one of their main characteristics. To the best of our knowledge this property has…
The coupled Stuart-Landau equation serves as a fundamental model for exploring synchronization and emergent behavior in complex dynamical systems. However, understanding its dynamics from a comprehensive nonlinear perspective remains…
A multi-dimensional switched system or multi-mode multi-dimensional ($M^3D$) system extends the classic switched system by allowing different subsystem dimensions. The stability problem of the $M^3D$ system, whose state transitions at…
Spontaneous emergence of organized states in materials driven by non-equilibrium conditions is of significant fundamental and technological interest. In many cases, the organized states are complex, hence, with some well-studied exceptions,…
Despite their apparent simplicity, random Boolean networks display a rich variety of dynamical behaviors. Much work has been focused on the properties and abundance of attractors. We here derive an expression for the number of attractors in…
We consider a one-dimensional directional array of diffusively coupled oscillators. They are perturbed by the injection of a small additive noise, typically orders of magnitude smaller than the oscillation amplitude, and the system is…
Recent advances in designing meta-materials have demonstrated that global mechanical properties of disordered spring networks can be tuned by selectively modifying only a small subset of bonds. Here, using a computationally-efficient…
The advances in understanding complex networks have generated increasing interest in dynamical processes occurring on them. Pattern formation in activator-inhibitor systems has been studied in networks, revealing differences from the…
In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod's necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated…
Whereas the importance of transient dynamics to the functionality and management of complex systems has been increasingly recognized, most of the studies are based on models. Yet in realistic situations the models are often unknown and what…
The dynamics of filaments in flow are central to understanding a wide range of biological and soft-matter systems, yet their behavior under time-dependent forcing remains poorly understood. Here, we investigate the long-time dynamics of…
The introduction of a memristor in a chaotic system can significantly modify its dynamical behavior. In this paper, we couple a discrete memristor model with a chaotic map to investigate the memristor's impact on the stability of chaotic…
The response of driven frustrated media stems from interacting hysteretic elements. We derive explicit mappings from networks of hysteretic springs to their abstract representation as interacting hysterons. These maps reveal how the…
We investigate classes of interacting systems that allow for a mapping to disordered noninteracting systems. As we show, such a mapping is possible for interacting systems with a suppressed density of states at the chemical potential,…
Neural dynamical systems with stable attractor structures, such as point attractors and continuous attractors, are hypothesized to underlie meaningful temporal behavior that requires working memory. However, working memory may not support…
We study dense mixtures of passive and active self-aligning disks with isotropic or anisotropic mobility. We find that the passive fraction controls an order-disorder transition that is continuous in the isotropic case and discontinuous in…
Many biological and synthetic systems are suspensions of oriented, actively-moving components. Unlike in passive suspensions, the interplay between orientational order, active flows, and interactions with boundaries gives rise to…
We study a one-dimensional system of spatially extended particles, which are fixated to regularly spaced locations by means of elastic springs. The particles are assumed to be driven by a Gaussian noise and to have dissipative,…
We examine a model system where attractors may consist of a heteroclinic cycle between chaotic sets; this `cycling chaos' manifests itself as trajectories that spend increasingly long periods lingering near chaotic invariant sets…