Related papers: A hierarchical heteroclinic network: Controlling t…
The possibility that evolutionary forces -- together with a few fundamental factors such as thermodynamic constraints, specific computational features enabling information processing, and ecological processes -- might constrain the logic of…
Heteroclinic cycles and networks are structures in dynamical systems composed of invariant sets and connecting heteroclinic orbits, and can be robust in systems with invariant subspaces. The usual method for analysing the stability of…
Heteroclinic cycles are widely used in neuroscience in order to mathematically describe different mechanisms of functioning of the brain and nervous system. Heteroclinic cycles and interactions between them can be a source of different…
The biological requirements for an ecosystem to develop and maintain species diversity are in general unknown. Here we consider a model ecosystem of sessile and mutually excluding organisms competing for space [Mathiesen et al. Phys. Rev.…
We develop a principled mathematical framework for controlling nonlinear, networked dynamical systems. Our method integrates dimensionality reduction, bifurcation theory and emerging model discovery tools to find low-dimensional subspaces…
Many natural and engineered complex networks have intricate mesoscopic organization, e.g., the clustering of the constituent nodes into several communities or modules. Often, such modularity is manifested at several different hierarchical…
Network structure or connectivity pattern is critical in determining collective dynamics among interacting species in ecosystems. Conventional research on species persistence in spatial populations has focused on static network structure,…
We study the evolution of networks through `triplets' - three-node graphlets. We develop a method to compute a transition matrix to describe the evolution of triplets in temporal networks. To identify the importance of higher-order…
We study heteroclinic networks in $\mathbb{R}^4$, made of a certain type of simple robust heteroclinic cycle. In simple cycles all the connections are of saddle-sink type in two-dimensional fixed-point spaces. We show that there exist only…
We show that heterodimensional cycles can be born at the bifurcations of a pair of homoclinic loops to a saddle-focus equilibrium for flows in dimension 4 and higher. In addition to the classical heterodimensional connection between two…
We describe a simple adaptive network of coupled chaotic maps. The network reaches a stationary state (frozen topology) for all values of the coupling parameter, although the dynamics of the maps at the nodes of the network can be…
Coexistence of individuals with different species or phenotypes is often found in nature in spite of competition between them. Stable coexistence of multiple types of individuals have implications for maintenance of ecological biodiversity…
This paper analyses the stability of cycles within a heteroclinic network lying in a three-dimensional manifold formed by six cycles, for a one-parameter model developed in the context of game theory. We show the asymptotic stability of the…
Ecological systems comprise an astonishing diversity of species that cooperate or compete with each other forming complex mutual dependencies. The minimum requirements to maintain a large species diversity on long time scales are in general…
Formation and competition of associations are studied in a six-species ecological model where each species has two predators and two prey. Each site of a square lattice is occupied by an individual belonging to one of the six species. The…
In this work we give specific examples of competition models, with six and eight species, whose three-dimensional dynamics naturally leads to the formation of string networks with junctions, associated with regions that have a high…
We consider networks of dynamical units that evolve in time according to different laws, and are coupled to each other in highly irregular ways. Studying how to steer the dynamics of such systems towards a desired evolution is of great…
Conditions are provided under which lack of domination of a homoclinic class yields robust heterodimensional cycles. Moreover, so-called viral homoclinic classes are studied. Viral classes have the property of generating copies of…
How large ecosystems can create and maintain the remarkable biodiversity we see in nature is probably one of the biggest open questions in science, attracting attention from different fields, from Theoretical Ecology to Mathematics and…
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…