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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…

We conceive finite automata as dynamical systems on discontinuum and investigate their factors. Factors of finite automata include many well-known simple dynamical systems, e.g. hyperbolic systems and systems with finite attractors. In the…

We give necessary and/or sufficient conditions for stochastic stability of second-order linear autonomous systems with parameters, which are perturbed by a random process of the "white noise" type. The Ito's and Stratonovich's forms of…

The behavior of homogeneous and disordered systems with a free boundary is described on the basis of group theory in the two-loop approximation directly in three-dimensional space. The effect of the free boundary on the regime of the bulk…

Patterns in reaction-diffusion systems often contain two spatial scales; a long scale determined by a typical wavelength or domain size, and a short scale pertaining to front structures separating different domains. Such patterns naturally…

We conjecture that chaotic resonance modes in scattering systems are a product of a conditionally invariant measure from classical dynamics and universal exponentially distributed fluctuations. The multifractal structure of the first factor…

Summary: A system of autonomous ordinary differential equations depending on a small parameter is considered such that the unperturbed system has an invariant manifold of periodic solutions that is not normally hyperbolic but is normally…

The paper is focused on the discussion of the phenomenon of transitional chaos in dynamic autonomous and non-autonomous systems. This phenomenon involves the disappearance of chaotic oscillations in specific time periods and the system…

We introduce a new analytical method, which allows to find out chaotic dynamics in non-smooth dynamical systems. A simple mechanical system consisting of a mass and a dry friction element is considered as an example. The corresponding…

This paper investigates the origin and onset of chaos in a mathematical model of an individual neuron, arising from the intricate interaction between 3D fast and 2D slow dynamics governing its intrinsic currents. Central to the chaotic…

This paper deals with the problem of limit cycle bifurcations for piecewise smooth integrable differential systems with four zones. When the unperturbed system has a family of periodic orbits, the first order Melnikov function is derived…

Nonsmooth formulations of physical models are common, particularly in climate modeling. However, in many of these models, there is little justification for this modeling choice, and no mathematical indication that the resulting behavior in…

[This is the unpublished supplemental information from 1989 to the paper: J.M. Deutsch, "Quantum statistical mechanics in a closed system." Phys. Rev. A, 43(4), 2046 (1991).] A closed quantum mechanical system does not necessarily give time…

Spatio-temporal chaos in parametrically driven waves is investigated in one and two dimensions using numerical simulations of Ginzburg-Landau equations. A regime is identified in which in one dimension the dynamics are due to double phase…

The induction motor controlled by Indirect Field Oriented Control (IFOC) is known to have high performance and better stability. This paper reports the dynamical behavior of an indirect field oriented control (IFOC) induction motor drive in…

We report on the numerical and theoretical study of the subcritical bifurcation of parametrically amplified waves appearing at the interface between two immiscible incompressible fluids when the layer of the lower fluid is very shallow. As…

We investigate the slow passage through a pitchfork bifurcation in a spatially extended system, when the onset of instability is slowly varying in space. We focus here on the critical parameter scaling, when the instability locus propagates…

In this work we provide an overview of jamming transitions in two dimensional systems focusing on the limit of frictionless particle interactions in the absence of thermal fluctuations. We first discuss jamming in systems with short range…

This Letter outlines 20 geometric mechanisms by which limit cycles are created locally in two-dimensional piecewise-smooth systems of ODEs. These include boundary equilibrium bifurcations of hybrid systems, Filippov systems, and continuous…

Chemical, physical and ecological systems passing through a saddle-node bifurcation will, momentarily, find themselves balanced at a semi-stable steady state. If perturbed by noise, such systems will escape from the zero-steady state, with…