The interdisciplinary journal of Discontinuity, Nonlinearity, and Complexity 

About: The interdisciplinary journal of Discontinuity, Nonlinearity, and Complexity is an academic journal published by L&H Scientific Publishing LLC. The journal publishes majorly in the area(s): Nonlinear system & Computer science. It has an ISSN identifier of 2164-6376. Over the lifetime, 252 publications have been published receiving 764 citations. The journal is also known as: Discontinuity, nonlinearity and complexity & Discontinuity, nonlinearity, and complexity.

Fractional Maps and Fractional Attractors. Part I: $α$-Families of Maps

Abstract: In this paper we present a uniform way to derive families of maps from the corresponding differential equations describing systems which experience periodic kicks. The families depend on a single parameter - the order of a differential equation $\\alpha > 0$. We investigate general properties of such families and how they vary with the increase in $\\alpha$ which represents increase in the space dimension and the memory of a system (increase in the weights of the earlier states). To demonstrate general properties of the $\\alpha$-families we use examples from physics (Standard $\\alpha$-family of maps) and population biology (Logistic $\\alpha$-family of maps). We show that with the increase in $\\alpha$ systems demonstrate more complex and chaotic behavior.

Method of conservation laws for constructing solutions to systems of PDEs

Abstract: In the present paper, a new method is proposed for constructing exact solutions for systems of nonlinear partial differential equations. It is called the method of conservation laws. Application of the method to the Chaplygin gas allowed to construct new solutions containing several arbitrary parameters. It is shown that these solutions cannot be obtained, in general, as group invariant solutions.

Automatic recognition and tagging of topologically different regimes in dynamical systems

Abstract: Complex systems are commonly modeled using nonlinear dynamical systems. These models are often high-dimensional and chaotic. An important goal in studying physical systems through the lens of mathematical models is to determine when the system undergoes changes in qualitative behavior. A detailed description of the dynamics can be difficult or impossible to obtain for high-dimensional and chaotic systems. Therefore, a more sensible goal is to recognize and mark transitions of a system between qualitatively different regimes of behavior. In practice, one is interested in developing techniques for detection of such transitions from sparse observations, possibly contaminated by noise. In this paper we develop a framework to accurately tag different regimes of complex systems based on topological features. In particular, our framework works with a high degree of success in picking out a cyclically orbiting regime from a stationary equilibrium regime in high-dimensional stochastic dynamical systems.