相关论文: ChaNoXity: The Nonlinear Dynamics of Nature

Different aspects of the predictability problem in dynamical systems are reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy, Shannon entropy and algorithmic complexity is discussed. In particular, we emphasize…

The unreduced, universally nonperturbative analysis of arbitrary many-body interaction process reveals the irreducible, purely dynamic source of randomness. It leads to the universal definition of real system complexity (physics/9806002),…

From the equations of conservation laws for energy, linear momentum, angular momentum and mass the evolutionary relation in differential forms follows. This relation connects the differential of entropy and the skew-symmetric form, whose…

We investigate the non-uniqueness of weak solutions of the Quantum-Hydrodynamic system. This form of ill-posedness is related to the change of the number of connected components of the support of the position density (called nodal domains)…

We present a simple physical model that recapitulates several features of biological evolution, while being based only on thermally-driven attachment and detachment of elementary building blocks. Through its dynamics, this model samples a…

Within the frames of the analytical mechanics the method of the description of dynamics of nonequilibrium systems of potentially interacting elements is develops. The method is based on an opportunity of representation of nonequilibrium…

It is increasingly evident that there is more to biological evolution than natural selection; moreover, the concept of evolution is not limited to biology. We propose an integrative framework for characterizing how entities evolve, in which…

The roughness of vapor-deposited thin films can display a nonmonotonic dependence on film thickness, if the smoothening of the small-scale features of the substrate dominates over growth-induced roughening in the early stage of evolution.…

We study the dynamics of a non-minimally coupled scalar field cosmology with a potential function. We use the framework of dynamical systems theory to investigate all evolutional paths admissible for all initial conditions. Additionally, we…

Predicting the evolution of systems that exhibit spatio-temporal dynamics in response to external stimuli is a key enabling technology fostering scientific innovation. Traditional equations-based approaches leverage first principles to…

This thesis is concerned with dynamics of conservative nonlinear waves on bounded domains. In general, there are two scenarios of evolution. Either the solution behaves in an oscillatory, quasiperiodic manner or the nonlinear effects cause…

Biological activities are often seen entrained onto the day-night and other celestial mechanical cycles (e.g., seasonal and lunar), but studies on the origin of life have largely not accounted for such periodic external environmental…

Presented theory of feelings and emotions is based on Nonlinear Dynamics and Theory of Complex Systems. The most important assumption is that the brain may be considered to be composed of subsystems characterized by different characteristic…

We here describe the possibility of a synthetic description of the onset of Chaos in many degrees of freedom dynamical systems within the framework of the geometric description of dynamics. We show how this approach to instability helps to…

Life is fundamentally a scientific enigma. The interplay between chaos, entropy dynamics, and Prigogine's dissipative systems offers profound insights into the emergence, stabilization, and eventual collapse of far-from-equilibrium systems.…

Noise is a ubiquitous feature of the physical world. As a result, the first prerequisite of life is fault tolerance: maintaining integrity of state despite external bombardment. Recent experimental advances have revealed that biological…

We study the effects produced by competition of two physical mechanisms of energy localization in inhomogeneous nonlinear systems. As an example, we analyze spatially localized modes supported by a nonlinear impurity in the generalized…

We study the structure and stability of nonlinear impurity modes in the discrete nonlinear Schr{\"o}dinger equation with a single on-site nonlinear impurity emphasizing the effects of interplay between discreteness, nonlinearity and…

We introduce structural heterogeneity, a new topological characteristic for semi-ordered materials that captures their degree of organisation at a mesoscopic level and tracks their time-evolution, ultimately detecting the order-disorder…

Here we postulate three laws which form a mathematical framework to capture the essence of Darwinian evolutionary dynamics. The second law is most quantitative and is explicitly expressed by a unique form of stochastic differential…