Related papers: Ghost states underlying spatial and temporal patte…
We give a simple discussion of ghosts, unitarity violation, negative norm states and quantum vs classical behavior in the simplest model with four derivative action - the Pais-Uhlenbeck oscillator. We also point out that the normalizable…
We propose a new simple three-dimensional continuous autonomous model with two nonlinear terms and observe the dynamical behavior with respect to system parameters. This system changes the stability of fixed point via Hopf bifurcation and…
This paper addresses the challenge of time-inconsistent stochastic control within a continuous-time framework. Its primary focus lies in uncovering a probabilistic representation, specifically in the shape of a system of backward stochastic…
We study the linear perturbations about nonrotating black holes in the context of degenerate higher-order scalar-tensor (DHOST) theories, using a systematic approach that extracts the asymptotic behaviour of perturbations (at spatial…
Data-driven modelling and scientific machine learning have been responsible for significant advances in determining suitable models to describe data. Within dynamical systems, neural ordinary differential equations (ODEs), where the system…
We present a study of the recently discovered spatially-extended chaotic state known as spiral-defect chaos, which occurs in low-Prandtl-number, large-aspect-ratio Rayleigh-Benard convection. We employ the modulus squared of the space-time…
The path integral for ghost fermions, which is heuristically made use of in the Batalin- Fradkin-Vilkovisky approach to quantization of constrained systems, is derived from first principles. The derivation turns out to be rather different…
Understanding neural dynamics is a central topic in machine learning, non-linear physics and neuroscience. However, the dynamics is non-linear, stochastic and particularly non-gradient, i.e., the driving force can not be written as gradient…
In the context of Degenerate Higher-Order Scalar-Tensor (DHOST) theories, we study cosmological solutions and their stability properties. In particular, we explicitly illustrate the crucial role of degeneracy by showing how the higher order…
This article establishes the foundation for a new theory of invariant/integral manifolds for non-autonomous dynamical systems. Current rigorous support for dimensional reduction modelling of slow-fast systems is limited by the rare events…
Small-sized systems exhibit a finite number of routes to chaos. However, in extended systems, not all routes to complex spatiotemporal behavior have been fully explored. Starting from the sine-Gordon model of parametrically driven chain of…
The self-accelerating universe realizes the accelerated expansion of the universe at late times by large-distance modification of general relativity without a cosmological constant. The Dvali-Gabadadze-Porrati (DGP) braneworld model…
Investigating the possibility of applying techniques from linear systems theory to the setting of nonlinear systems has been the focus of many papers. The pseudo linear form representation of nonlinear dynamical systems has led to the…
We introduce a minimization formulation for the determination of a finite-dimensional, time-dependent, orthonormal basis that captures directions of the phase space associated with transient instabilities. While these instabilities have…
Active systems are comprised of constituents with interactions that are generically non-reciprocal in nature. Such non-reciprocity often gives rise to situations where conflicting objectives exist, such as in the case of a predator pursuing…
The limiting slow dynamics of slow-fast, piecewise-linear, continuous systems of ODEs occurs on critical manifolds that are piecewise-linear. At points of non-differentiability, such manifolds are not normally hyperbolic and so the…
Dynamics in delayed differential equations (DDEs) is a well studied problem mainly because DDEs arise in models in many areas of science including biology, physiology, population dynamics and engineering. The change of nature in the…
Recent progress of symbolic dynamics of one- and especially two-dimensional maps has enabled us to construct symbolic dynamics for systems of ordinary differential equations (ODEs). Numerical study under the guidance of symbolic dynamics is…
We explore the real solutions to the Spherical Collapse Model in a non-flat Universe with a Cosmological Constant, and observe a possible situation for a fake or Ghost Collapse, in which an expanding overdense spherical region, turns around…
A two-dimensional small-world type network, subject to spatial prisoners' dilemma dynamics and containing an influential node defined as a special node with a finite density of directed random links to the other nodes in the network, is…