Related papers: ChaNoXity: The Nonlinear Dynamics of Nature
We apply the formalism of dynamical system analysis to investigate the evolution of interacting dark energy scenarios at the background and perturbation levels in a unified way. Since the resulting dynamical system contains the extra…
Active matter has played a pivotal role in advancing our understanding of non-equilibrium systems, leading to a fundamental shift in the study of biophysical phenomena. The foundation of active matter research is built on assumptions…
The dynamical ellipticity of a planet expresses the departure of its mass distribution from spherical symmetry. It enters as a parameter in the description of a planet's precession and nutation, as well as other rotational normal modes. In…
In this work, we perform a detailed dynamical analysis for the cosmological applications of a nonminimal torsion-matter coupled gravity. Two alternative formalisms are proposed, which enable one to choose between the easier approach for a…
This paper discusses three new issues that necessarily arise in realistic attempts to apply nonlinear dynamics to galaxy evolution, namely: (i) the meaning of chaos in many-body systems, (ii) the time-dependence of the bulk potential, which…
We investigate instability phenomena for linear evolution equations within the framework of $C_0$--semigroups on infinite--dimensional spaces. We show that Devaney chaos, being formulated in purely topological terms, may depend on the…
We review the concept of well-posedness in the context of evolutionary problems from mathematical physics for a particular subclass of problems from elasticity theory. The complexity of physical phenomena appears as encoded in so called…
Non-commutative propositions are characteristic of both quantum and non-quantum (sociological, biological, psychological) situations. In a Hilbert space model states, understood as correlations between all the possible propositions, are…
The analysis of riverbed evolution is an important basis for decision-making on river improvement, flood control project construction, and water conservancy hub dispatching and application. From the perspective of river nonlinear dynamic…
This paper formulates a new approach to the study of chaos in discrete dynamical systems based on the notions of inverse ill-posed problems, set-valued mappings, generalized and multivalued inverses, graphical convergence of a net of…
When complex systems are driven to extinction by some external factor, their non-stationary dynamics can present an intermittent behaviour between relative tranquility and burst of activity whose consequences are often catastrophic. To…
We develop an theoretical approach for predicting biodiversity in multi-dimensional niche spaces, arising due to ecological drivers such as competitive exclusion. The novelty of our approach relies on the fact that ecological niches are…
Caustics are a generic feature of the nonlinear growth of structure in the dark matter distribution. If the dark matter were absolutely cold, its mass density would diverge at caustics, and the integrated annihilation probability would also…
We argue that the spatial discretization of the strongly nonlinear Lefever-Lejeune partial differential equation defines a nonlinear lattice that is physically relevant in the context of the nonlinear physics of ecosystems, modelling the…
Nonlinear dynamics (``chaos theory'') and quantum mechanics are two of the scientific triumphs of the 20th century. The former lies at the heart of the modern interdisciplinary approach to science, whereas the latter has revolutionized…
Living systems self-organize in ways that conventional physical frameworks-based on forces, energies, and continuous fields-cannot fully capture. Processes like gene regulation and cellular decision-making involve rule-based logic and…
We discuss some important issues arising from computational efforts in dynamical systems and fluid dynamics. Various individuals have misunderstood these issues since the onset of these problem areas; indeed, they have been routinely…
Shape dynamics is an alternative background-independent approach to classical dynamics that implements Leibnizian philosophy and Mach's Principles. It is a formulation of the dynamics of the universe in terms of the intrinsic and relational…
Instabilities driven by strong gradients appear in a wide variety of physical systems, including plasmas, neutral fluids, and self-gravitating systems. This work develops an analytic formulation to describe the transport structure and…
The paper discusses the basic paradoxes of thermodynamics and quantum mechanics. The approaches to solution of these paradoxes are suggested. The first one relies on the influence of the external observer (environment), which disrupts the…