Related papers: Distorted stability pattern and chaotic features f…
A two-dimensional homomorphic logistic map that preserves features of the Lotka-Volterra equations was proposed. To examine chaos, iteration plots of the population, Lyapunov exponents calculated from Jacobian eigenvalues of the $2$D…
We investigate universal features of measurement-and-feedback control of quantum chaotic dynamics by examining the quantum Arnold cat map, a paradigmatic model of quantum chaos. Inspired by probabilistic control of classical chaos, our…
We extend the Wigner-Weyl-Moyal phase-space formulation of quantum mechanics to general curved configuration spaces. The underlying phase space is based on the chosen coordinates of the manifold and their canonically conjugate momenta. The…
In this work, we examine a kinetic framework for modeling the time evolution of size distribution densities of two populations governed by predator-prey interactions. The model builds upon the classical Boltzmann-type equations, where the…
Our recent work lays out a general framework for inferring information about the parameters and associated dynamics of a differential equation model from a discrete set of data points collected from the system being modeled. Rigorous…
The damping of the harmonic oscillator is studied in the framework of the Lindblad theory for open quantum systems. A generalization of the fundamental constraints on quantum mechanical diffusion coefficients which appear in the master…
This paper is concerned with the Wigner-Poisson-Fokker-Planck system, a kinetic evolution equation for an open quantum system with a non-linear Hartree potential. Existence, uniqueness and regularity of global solutions to the Cauchy…
This paper tackles Hamiltonian chaos by means of elementary tools of Riemannian geometry. More precisely, a Hamiltonian flow is identified with a geodesic flow on configuration space-time endowed with a suitable metric due to Eisenhart.…
The broad application range of the predator-prey modelling enabled us to apply it to represent the dynamics of the work-employment system. For the adopted period, we conclude that this dynamics is chaotic in the beginning of the time series…
We construct and study perturbative unitarity (i.e., ghost and tachyon analysis) of a $3+1$-dimensional noncompact Weyl-Einstein-Yang-Mills model. The model describes a local noncompact Weyl's scale plus $SU(N)$ phase invariant Higgs-like…
In this work, we consider a system of differential equations modeling the dynamics of some populations of preys and predators, moving in space according to rapidly oscillating time-dependent transport terms, and interacting with each other…
We present a computational framework to investigate steady state distributions and perform stability analysis for random ordinary differential equations driven by parameter uncertainty. Using the nonlinear Rosenzweig McArthur predator prey…
A new non-perturbative approach to quantum theory in curved spacetime and to quantum gravity, based on a generalisation of the Wigner equation, is proposed. Our definition for a Wigner equation differs from what have otherwise been…
We elucidate the basic physical mechanisms responsible for the quantum-classical transition in one-dimensional, bounded chaotic systems subject to unconditioned environmental interactions. We show that such a transition occurs due to the…
Classically chaotic systems relax to coarse grained states of equilibrium. Here we numerically study the quantization of such bounded relaxing systems, in particular the quasi-periodic fluctuations associated with the correlation between…
Field theory tools are applied to analytically study fluctuation and correlation effects in spatially extended stochastic predator-prey systems. In the mean-field rate equation approximation, the classic Lotka-Volterra model is…
Starting from a generalization of Weyl's relations in finite dimension $N$, we show that the Heisenberg commutation relations can be satisfied in a specific $N-1$ dimensional subspace, and display a linear map for projecting operators to…
The forces which drive growth, development, survival and change within an ecological system involving a predator and prey specie are not easily addressed in the field. To better understand the dynamics in the system, ecologists have turned…
We consider stability in a class of random non-linear dynamical systems characterised by a relaxation rate together with a Gaussian random vector field which is white-in-time and spatial homogeneous and isotropic. We will show that in the…
We begin with a review of the statements of non-linear, linear and mode stability of autonomous dynamical systems in classical mechanics, using symplectic geometry. We then discuss what the phase space and the Hamiltonian of general…