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In this paper the complex dynamical analysis of the parametric fourth-order Kim's iterative family is made on quadratic polynomials, showing the Matlab codes generated to draw the fractal images necessary to complete the study. The…
We explore the dynamical behaviour of cosmological models involving a scalar field (with an exponential potential and a canonical kinetic term) and a matter fluid with spatial curvature included in the equations of motion. Using…
A criterion on the asymptotic stability of fractional-order systems with incomensurate orders is proposed in this paper. Existing methods always assume order parameters be rational numbers or the ratios of any two orders be rational…
The paper deals with a new sharp criterion ensuring the Aubin property of solution maps to a class of parameterized variational systems. This class includes parameter-dependent variational inequalities with non-polyhedral constraint sets…
We apply polynomial techniques (linear programming) to obtain lower and upper bounds on the covering radius of spherical designs as function of their dimension, strength, and cardinality. In terms of inner products we improve the lower…
Frequency responses of multi-degree-of-freedom mechanical systems with weak forcing and damping can be studied as perturbations from their conservative limit. Specifically, recent results show how bifurcations near resonances can be…
We present a combinatorial approach to rigorously show the existence of fixed points, periodic orbits, and symbolic dynamics in discrete-time dynamical systems, as well as to find numerical approximations of such objects. Our approach…
Baroclinic instability is a fundamental mechanism driving atmospheric dynamics. In this work, we revisit Pedlosky's two-layer model for finite amplitude baroclinic waves - a seminal framework for studying the unstable growth of finite…
Using a solvable model, the two-dimensional two-component plasma, we study a Coulomb gas confined in a disk and in an annulus with boundaries that can adsorb some of the negative particles of the system. We obtain explicit analytic…
Area preserving maps provide the simplest and most accurate means to visualize and quantify the behavior of nonlinear systems. Convenience of the mapping equations of motion for investigation of transition to chaotic behavior in dynamics of…
Nonlinear dynamics plays a significant role in interdisciplinary fields spanning biology, engineering, mathematics, and physics. Under small-amplitude approximations, certain nonlinear systems can be effectively described by the linear…
Colloidal suspensions have long been studied as a model for atomic and molecular systems, due to the ability to fluorescently label and individually track each particle, yielding particle-resolved structural information. This allows various…
We study the two-dimensional border-collision normal form (a four-parameter family of continuous, piecewise-linear maps on $\mathbb{R}^2$) in the robust chaos parameter region of [S. Banerjee, J.A. Yorke, C. Grebogi, Robust Chaos, Phys.…
Many statistical models are algebraic in that they are defined by polynomial constraints or by parameterizations that are polynomial or rational maps. This opens the door for tools from computational algebraic geometry. These tools can be…
In this paper, we analyze the stochastic properties of some large size (area) polyominoe's perimeter such that the directed column-convex polyomino, the column-convex polyomino, the directed diagonally-convex polyomino, the staircase (or…
We suggest and describe the protocol of measurements providing completely probabilistic representation of all parameters of biphoton polarization qutrits, i.e providing explicit expressions for all parameters of qutrits via the…
A recently developed method has been extended to a nonlocal equation arising in steady water wave propagation in two dimensions. We obtain analyic approximation of steady water wave solution in two dimensions with rigorous error bounds for…
The system in which a small rigid ball is bouncing repeatedly on a massive at table vibrating vertically, so-called the bouncing ball system, has been widely studied. Under the assumption that the table is vibrating with a piecewise…
The various phase spaces involved in the dynamics of parametrized nonrelativistic Hamiltonian systems are displayed by using Crnkovic and Witten's covariant canonical formalism. It is also pointed out that in Dirac's canonical formalism…
An explicit expression in terms of canonical variables is obtained for the Hamiltonian functional determining the fully nonlinear dynamics of two-dimensional potential flows of an ideal fluid with a free surface over an arbitrary nonuniform…