We study a fast-slow version of an SIRS epidemiological model on homogeneous graphs, obtained through the application moment closure method. use GSPT to model, taking into account that infection period is much shorter than average duration immunity. show dynamics occurs sequence fast and slow flows, can be described 2-dimensional maps that, under some assumptions, approximated as 1-dimensional maps. Using this method, together with numerical bifurcation tools, we give rise periodic...

Laplacian dynamics on a signless graph characterize class of linear interactions, where pairwise cooperative interactions between all agents lead to the convergence common state. On structurally balanced signed graph, converge values same magnitude but opposite signs (bipartite consensus), as illustrated by well-known Altafini model. These have been modeled using traditional graphs, relationships are always pairwise. In comparison, higher-order networks (such hypergraphs), offer possibility...

Oscillatory behavior is ubiquitous in many natural and engineered systems, often emerging through self-regulating mechanisms. In this paper, we address the challenge of stabilizing a desired oscillatory pattern networked system where neither internal dynamics nor interconnections can be changed. To achieve this, propose two distinct control strategies. The first requires full knowledge generating pattern, while second only needs local error information. addition, controllers are implemented...

It is known that a linear system with matrix A constitutes Hamiltonian quadratic if and only matrix. This provides straightforward method to verify whether or given function corresponds system. These techniques fundamentally rely on the properties of matrices. Building recent advances in tensor algebra, this paper generalizes such results broad class polynomial systems. As systems interest can be naturally represented forms, we name them tensor-based Our main contribution formally define...

We have developed Simulation-based Reconstructed Diffusion (SbRD) to determine diffusion coefficients corrected for confinement effects and the bias introduced by two-dimensional models describing a three-dimensional motion. validate method on simulated data in cell-shaped compartments. use SbRD, combined with new cell detection method, of set native proteins Escherichia coli. observe slower at poles than nucleoid region exponentially growing cells, which is independent presence polysomes....

In this letter, we investigate a class of slow-fast systems for which the classical model order reduction technique based on singular perturbations does not apply due to lack normally hyperbolic critical manifold. We show, however, that there exists after well-defined change coordinates have This allows use techniques and qualitatively describe dynamics from auxiliary reduced models even in neighborhood non-hyperbolic point. As an important consequence step, show it is possible design...

In graph-theoretical terms, an edge in a graph connects two vertices while hyperedge of hypergraph any more than one vertices. If the hypergraph's hyperedges further connect same number vertices, it is said to be uniform. algebraic theory, can characterized by adjacency matrix, and similarly, uniform tensor. This similarity enables us extend existing tools matrix analysis for studying dynamical systems evolving on graphs study class polynomial hypergraphs utilizing properties tensors. To...

It is known that the effect of species' density on growth non-additive in real ecological systems. This challenges conventional Lotka-Volterra model, where interactions are always pairwise and their effects additive. To address this challenge, we introduce HOIs (Higher-Order Interactions) which able to capture, for example, indirect one species a second correlating third species. Towards end, propose general higher-order model. We provide an existence result positive equilibrium...

In this paper we explore the methodology of model order reduction based on singular perturbations for a flexible-joint robot within port-Hamiltonian framework. We show that has representation which is also singularly perturbed ordinary differential equation. Moreover, associated reduced slow subsystem corresponds to rigid-joint robot. To exploit usefulness models, provide numerical example where an existing controller rigid implemented.

While conventional graphs only characterize pairwise interactions, higher-order networks (hypergraph, simplicial complex) capture multi-body which is a potentially more suitable modeling framework for complex real system. However, the introduction of interactions brings new challenges rigorous analysis such systems on network. In this paper, we study series SIS-type diffusion processes with both indirect and direct pathways directed hypergraph. concrete case, model propose based specific...

We study fast-slow maps obtained by discretization of planar systems in continuous time. focus on describing the so-called delayed loss stability induced slow passage through a singularity systems. This can be related to presence canard solutions. Here we consider three types singularities: transcritical, pitchfork, and fold. First, show that under an explicit Runge--Kutta delay stability, due transcritical or pitchfork singularity, arbitrarily long. In contrast, prove Kahan--Hirota--Kimura...

We study generic constrained differential equations (CDEs) with three parameters, thereby extending Takens's classification of singularities such equations. In this approach, the analyzed are Swallowtail, Hyperbolic, and Elliptic Umbilics. provide polynomial local normal forms CDEs under topological equivalence. Generic important in slow–fast (SF) systems. Many properties characteristic behavior solutions SF systems can be inferred from corresponding CDE. Therefore, results paper show a...

Network dynamics is nowadays of extreme relevance to model and analyze complex systems. From a dynamical systems perspective, understanding the local behavior near equilibria utmost importance. In particular, with at least one zero eigenvalue play crucial role in bifurcation analysis. this paper, we want shed some light on nilpotent network As main result, show that blow-up technique, which has proven be extremely useful degenerate singularities low-dimensional ordinary differential...