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Adaptive transport networks in biological and physical systems exhibit hierarchical organization, characteristic channel spacing, and robust scaling relations. Existing adaptive network models, formulated on a lattice, successfully…
Regime shifts in biology, ecology, and other complex systems are often interpreted through stability landscapes and early warning signals that implicitly assume dynamics without memory effects. Yet many real systems exhibit these effects,…
Multistability, the coexistence of multiple stable states, is a cornerstone of nonlinear dynamical systems, governing their equilibrium, tunability, and emergent complexity. Recently, the concept of hidden multistability, where certain…
Resistive switching is one of the foremost candidates for building novel types of non-volatile random access memories. Any practical implementation of such a memory cell calls for a strong miniaturization, at which point fluctuations start…
We construct and analyze a rate-based neural network model in which self-interacting units represent clusters of neurons with strong local connectivity and random inter-unit connections reflect long-range interactions. When sufficiently…
Microfluidic systems are now being designed with precision to execute increasingly complex tasks. However, their operation often requires numerous external control devices due to the typically linear nature of microscale flows, which has…
We propose a methodology to analyze synchronization in an ensemble of diffusively coupled multistable systems. First, we study how two bidirectionally coupled multistable oscillators synchronize and demonstrate the high complexity of the…
We report an experimental evidence of a global bifurcation on a highly turbulent von Karman flow. The mean flow presents multiple solutions: the canonical symmetric solution becomes marginally unstable towards a flow which breaks the basic…
We report on an astonishing switching synchronization phenomenon in one-dimensional memristive networks, which occurs when several memristive systems with different switching constants are switched from the high to low resistance state. Our…
Semiconductor $p^+ - p^- - n - p^+ - n^{++}$ structures with large junction and contact areas are treated as 1 \times 2-dimensional active media, in which self-organized pattern formation can be expected. The local bistable behavior of the…
We give a nontechnical description of the behaviour of dynamical systems governed by two distinct time scales. We discuss in particular memory effects, such as bifurcation delay and hysteresis, and comment the scaling behaviour of…
Stochastic network-dynamics are typically assumed to be memory-less. Involving prolonged dwells interrupted by instantaneous transitions between nodes such Markov networks stand as a coarse-graining paradigm for chemical reactions, gene…
Oscillatory synchrony is hypothesized to support the flow of information between brain regions, with different phase-locked configurations enabling activation of different effective interactions. Along these lines, past work has proposed…
We show that a neural network originally designed for language processing can learn the dynamical rules of a stochastic system by observation of a single dynamical trajectory of the system, and can accurately predict its emergent behavior…
Complex networks encountered in biology are often characterized by significant structural diversity. Whether it be differences in the three-dimensional structure of allosteric proteins, or the variation among the micro-scale structures of…
Here we numerically study a model of excitable media, namely, a network with occasionally quiet nodes and connection weights that vary with activity on a short-time scale. Even in the absence of stimuli, this exhibits unstable dynamics,…
Active fluids, such as suspensions of microswimmers, are known to self-organize into complex spatio-temporal flow patterns. An intriguing example is mesoscale turbulence, a state of dynamic vortex structures exhibiting a characteristic…
We study the effect of varying wiring in excitable random networks in which connection weights change with activity to mold local resistance or facilitation due to fatigue. Dynamic attractors, corresponding to patterns of activity, are then…
Network theory is rapidly changing our understanding of complex systems, but the relevance of topological features for the dynamic behavior of metabolic networks, food webs, production systems, information networks, or cascade failures of…
When a fluid comprised of multiple phases or constituents flows through a network, non-linear phenomena such as multiple stable equilibrium states and spontaneous oscillations can occur. Such behavior has been observed or predicted in a…