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Superstatistics is a widely employed tool of non-equilibrium statistical physics which plays an important role in analysis of hierarchical complex dynamical systems. Yet, its "canonical" formulation in terms of a single nuisance parameter…
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…
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…
Self-adaptive systems continuously adapt to changes in their execution environment. Capturing all possible changes to define suitable behaviour beforehand is unfeasible, or even impossible in the case of unknown changes, hence human…
Recent measurements of durations of non-equilibrium processes provide valuable information on microscopic mechanisms and energetics. Comprehensive theory for corresponding experiments so far is well developed for single-particle systems…
A generic saddle-node bifurcation is proposed to modelize fast transitions of finite amplitude arising in geophysical (and perhaps other) contexts, when they result from the intrinsic dynamics of the system. The fast transition is…
In complex systems, external parameters often determine the phase in which the system operates, i.e., its macroscopic behavior. For nearly a century, statistical physics has extensively studied systems' transitions across phases,…
In self-gravitating stars, two dimensional or geophysical flows and in plasmas, long range interactions imply a lack of additivity for the energy; as a consequence, the usual thermodynamic limit is not appropriate. However, by contrast with…
The phase transitions and critical properties of two types of inhomogeneous systems are reviewed. In one case, the local critical behaviour results from the particular shape of the system. Here scale-invariant forms like wedges or cones are…
By integrating 4 lines of thoughts: symmetry breaking originally advanced by Anderson, bifurcation from nonlinear dynamics, Landau's theory of phase transition, and the mechanism of emergent rare events studied by Kramers, we introduce a…
A model of an organism as an autonomous intelligent system has been proposed. This model was used to analyze learning of an organism in various environmental conditions. Processes of learning were divided into two types: strong and weak…
Using in a simple way the theory of non linear dynamical systems, we show that increasing climatic instabilities may be a qualitative warning sign for the occurrence of a nearby bifurcation, yielding a discontinuous and sudden climate…
Catastrophic regime shifts in complex natural systems may be averted through advanced detection. Recent work has provided a proof-of-principle that many systems approaching a catastrophic transition may be identified through the lens of…
The paper gives a systematic analysis of singularities of transition processes in dynamical systems. General dynamical systems with dependence on parameter are studied. A system of relaxation times is constructed. Each relaxation time…
For a general class of translationally invariant systems with a specific category of nonlinearity in the output, this paper presents necessary and sufficient conditions for global observability. Critically, this class of systems cannot be…
An important challenge in several disciplines is to understand how sudden changes can propagate among coupled systems. Examples include the synchronization of business cycles, population collapse in patchy ecosystems, markets shifting to a…
Bistable autonomous systems can be found inmany areas of science. When the intrinsic noise intensity is large, these systems exhibits stochastic transitions from onemetastable steady state to another. In electronic bistable memories, these…
The theory of continuous phase transitions predicts the universal collective properties of a physical system near a critical point, which for instance manifest in characteristic power-law behaviours of physical observables. The…
Continuum elasticity is a powerful tool applicable in a broad range of physical systems and phenomena. Yet, understanding how and on what scales material disorder may lead to the breakdown of continuum elasticity is not fully understood. We…
We develop a gauge-invariant formalism for the study of density perturbations in a Friedmann-Robertson-Walker universe with multiple interacting fluids and/or scalar fields. We show how N scalar fields may be described by N kinetic fluids…