Related papers: Dynamics of non-autonomous systems with nested inv…
Simple nonlinear dynamical systems with multiple stable stationary states are often taken as models for switchlike biological systems. This paper considers the interaction of multiple such simple multistable systems when they are embedded…
We examine n component spin systems with arbitrary two spin interactions (of unspecified range) within a general framework to highlight some new subtleties present in incommensurate systems. We determine the ground states of all…
We describe an example of a $C^\infty$ diffeomorphism on a 7--manifold which has a compact invariant set such that uncountably many of its connected components are pseudocircles. (Any 7--manifold will suffice.) Furthermore, any…
A broad range of nonlinear processes over networks are governed by threshold dynamics. So far, existing mathematical theory characterizing the behavior of such systems has largely been concerned with the case where the thresholds are…
Quantum dynamics of strongly correlated systems is a challenging problem. Although the low energy fractional excitations of one dimensional integrable models are often well-understood, exploring quantum dynamics in these systems remains…
Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for…
Classical nonlinear theories are highly successful in describing far-from-equilibrium dynamics of magnets, encompassing phenomena such as parametric resonance, ultrafast switching, and even chaos. However, at ultrashort length and time…
For system of two ordinary differential equations of the second order representing autonomous non-conservative holonomic mechanical system, in case of dynamics such as one-frequency periodical oscillations, is found integrated invariant of…
The dynamics by iteration of a function on a compact metric space, sometimes called a cascade, can be extended to the dynamics of a closed relation on such a space. Here we apply this relation dynamics to study semiflows (and their relation…
Macroscopic features of dynamical systems such as almost-invariant sets and coherent sets provide crucial high-level information on how the dynamics organises phase space. We introduce a method to identify time-parameterised families of…
Stickiness is a well known phenomenon in which chaotic orbits expend an expressive amount of time in specific regions of the chaotic sea. This phenomenon becomes important when dealing with area-preserving open systems because, in this…
This paper investigates contraction properties of switched dynamical systems for the case that all modes are non-contracting, thereby extending existing results that require at least one mode to be contracting. Leveraging the property that…
We study the topological dynamics by iterations of a piecewise continuous, non linear and locally contractive map in a real finite dimensional compact ball. We consider those maps satisfying the "separation property": different continuity…
The fundamental model of a periodic structure is a periodic point set up to rigid motion or isometry. Our recent paper in SoCG 2021 defined isometry invariants (density functions), which are complete in general position and continuous under…
Nonlinear stripe patterns occur in many different systems, from the small scales of biological cells to geological scales as cloud patterns. They all share the universal property of being stable at different wavenumbers $q$, i.e., they are…
Hybrid (and impact) systems are dynamical systems experiencing both continuous and discrete transitions. In this work, we derive necessary and sufficient conditions for when a given differential form is invariant, with special attention…
We study the spin dynamics of quasi-one-dimensional F=1 condensates both at zero and finite temperatures for arbitrary initial spin configurations. The rich dynamical evolution exhibited by these non-linear systems is explained by…
In this paper we study topological and dynamical features of isolated invariant continua of continuous flows defined on surfaces. We show that near an isolated invariant continuum the flow is topologically equivalent to a C1 flow. We deduce…
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 investigate random complex dynamics of rational or polynomial maps on the Riemann sphere. We show that regarding random complex dynamics of polynomials, generically, the chaos of the averaged system disappears at any point in the Riemann…