Related papers: Global heteroclinic rebel dynamics among large 2-c…
The celebrated 1975 Kuramoto model of $N$ identical oscillators with phase angle vector $\boldsymbol{\vartheta}=(\vartheta_1,\ldots,\vartheta_N)$ and all-to-all coupling reads \begin{equation} \label{*}…
A six-dimensional reversible normal form system occurs in B{\'e}nard-Rayleigh convection between parallel planes, when we look for domain walls intersecting orthogonally (see Buffoni et al [1]). On the truncated system, we prove…
We study a system of coupled phase oscillators near a saddle-node on an invariant circle bifurcation and driven by random intrinsic frequencies. Under the variation of control parameters, the system undergoes a phase transition changing the…
An analytic reversible Hamiltonian system with two degrees of freedom is studied in a neighborhood of its symmetric heteroclinic connection made up of a symmetric saddle-center, a symmetric orientable saddle periodic orbit lying in the same…
We study two-cluster solutions of an ensemble of generic limit-cycle oscillators in the vicinity of a Hopf bifurcation, i.e. Stuart-Landau oscillators, with a nonlinear global coupling. This coupling leads to conserved mean-field…
We develop a path-integral formalism to study the formation of large-scale structures in the universe. Starting from the equations of motion of hydrodynamics (single-stream approximation) we derive the action which describes the statistical…
In this paper we examine robust clustering behaviour with multiple nontrivial clusters for identically and globally coupled phase oscillators. These systems are such that the dynamics is completely determined by the number of oscillators N…
The ubiquitous occurrence of cluster patterns in nature still lacks a comprehensive understanding. It is known that the dynamics of many such natural systems is captured by ensembles of Stuart-Landau oscillators. Here, we investigate…
Heteroclinic cycles are sequences of equilibria along with trajectories that connect them in a cyclic manner. We investigate a class of robust heteroclinic cycles that does not satisfy the usual condition that all connections between…
This paper is concerned with the theory of generic non-normal nonlinear evolutionary equations, with potential applications in Fluid Dynamics and Optics. Two theoretical models are presented. The first is a model two-level non-normal…
We analyze networked heterogeneous nonlinear systems, with diffusive coupling and interconnected over a generic static directed graph. Due to the network's hetereogeneity, complete synchronization is impossible, in general, but an emergent…
For percolating systems, we propose a universal exponent relation connecting the leading corrections to scaling of the cluster size distribution with the dynamic corrections to the asymptotic transport behaviour at criticality. Our…
We study bifurcation behavior in periodic perturbations of two-dimensional symmetric systems exhibiting codimension-two bifurcations with a double eigenvalue when the frequencies of the perturbation terms are small. We transform the…
This dissertation describes the space of heteroclinic orbits for a class of semilinear parabolic equations, focusing primarily on the case where the nonlinearity is a second degree polynomial with variable coefficients. Along the way, a new…
We study renormalization group multicritical fixed points in the $\epsilon$-expansion of scalar field theories characterized by the symmetry of the (hyper)cubic point group $H_N$. After reviewing the algebra of $H_N$-invariant polynomials…
We investigate a system of harmonically coupled identical nonlinear constituents subject to noise in different spatial arrangements. For global coupling we find for infinitely many constituents the coexistence of several ergodic components…
Heteroclinic structures organize global features of dynamical systems. We analyze whether heteroclinic structures can arise in network dynamics with higher-order interactions which describe the nonlinear interactions between three or more…
We show that any neighborhood of a non-degenerate reversible bifocal homoclinic orbit contains chaotic suspended invariant sets on $N$-symbols for all $N\geq 2$. This will be achieved by showing switching associated with networks of…
Using a variational method, we prove the existence of heteroclinic solutions for a 6dimensional system of ordinary differential equations. We derive this system from the classical B{\'e}nard-Rayleigh problem near the convective instability…
We study the emergence of symmetric oscillatory behavior in multi-agent systems where each agent incorporates a continuous memory of its past states and past rates of change, modeled by distributed retarded and neutral delays. The…