Related papers: The Inherent Instability of Disordered Systems
Turbulence follows a few well-known organizational principles, rooted in conservation laws. One such principle states that a system conserving two sign-definite invariants self-organizes into large-scale structures. Ordinary…
In this technical communique we study the maximal robust positively invariant set for state-constrained continuous-time nonlinear systems subjected to a bounded disturbance. Extending results from the theory of barriers, we show that this…
A necessary and sufficient condition for linear stability of inviscid parallel shear flow is formulated by developing a novel variational principle, where the velocity profile is assumed to be monotonic and analytic. It is shown that…
A celebrated and controversial hypothesis conjectures that some biological systems --parts, aspects, or groups of them-- may extract important functional benefits from operating at the edge of instability, halfway between order and…
The internal interactions of fluids occur at all scales therefore the resulting force fields have no reason to be smooth and differentiable. The release of the differentiability hypothesis has important mathematical consequences, like scale…
Smart matter consists of many sensors, computers and actuators embedded within materials. These microelectromechanical systems allow properties of the materials to be adjusted under program control. In this context, we study the behavior of…
We develop a general formalism for representing and understanding structure in complex systems. In our view, structure is the totality of relationships among a system's components, and these relationships can be quantified using information…
We investigate the selective forces that promote the emergence of modularity in nature. We demonstrate the spontaneous emergence of modularity in a population of individuals that evolve in a changing environment. We show that the level of…
The paper investigates dynamical systems for which the derivative of some positive-definite function along the solutions of this system depends on so-called density function. In turn, such dynamical systems are called density systems. The…
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…
Random matrix theory (RMT) provides a framework to study the spectral fluctuations in physical systems. RMT is capable of making predictions for the fluctuations only after the removal of the secular properties of the spectrum. Spectral…
We analyse a collection of empirical networks in a wide spectrum of disciplines and show that strong non-normality is ubiquitous in network science. Dynamical processes evolving on non-normal networks exhibit a peculiar behaviour, as…
Classical conditions for ensuring the robust stability of a linear system in feedback with a sector-bounded nonlinearity include small gain, circle, passivity, and conicity theorems. In this work, we present a similar stability condition,…
This paper proposes strategies for designing a system whose computational model is subject to aleatory and epistemic uncertainty. Aleatory variables, which are caused by randomness in physical parameters, are draws from a possibly unknown…
Recently it has been found that different physical systems driven by identical random noise behave exactly identical after a long time. It is also suggested that this is an outcome of finite precision in numerical experiments. Here we show…
Complex evolving systems such as the biosphere, ecosystems and societies exhibit sudden collapses, for reasons that are only partially understood. Here we study this phenomenon using a mathematical model of a system that evolves under…
The question how complex systems become more organized and efficient with time is open. Examples are, the formation of elementary particles from pure energy, the formation of atoms from particles, the formation of stars and galaxies, the…
Simplicity of fundamental physical laws manifests itself in fundamental symmetries. While systems with an infinity of strongly interacting degrees of freedom (in particle physics and critical phenomena) are hard to describe, they often…
The response of ecosystems to perturbations is considered from a thermodynamic perspective by acknowledging that, as for all macroscopic systems and processes, the dynamics and stability of ecosystems is subject to definite thermodynamic…
Based on extensive study of a dynamical systems model of the development of a cell society, a novel theory for stem cell differentiation and its regulation is proposed as the ``chaos hypothesis''. Two fundamental features of stem cell…