Related papers: A hierarchical heteroclinic network: Controlling t…
Network-theoretic tools contribute to understanding real-world system dynamics, e.g., in wildlife conservation, epidemics, and power outages. Network visualization helps illustrate structural heterogeneity; however, details about…
Learning or memory formation are associated with the strengthening of the synaptic connections between neurons according to a pattern reflected by the input. According to this theory a retained memory sequence is associated to a dynamic…
Networks provide a powerful formalism for modeling complex systems by using a model of pairwise interactions. But much of the structure within these systems involves interactions that take place among more than two nodes at once; for…
In this paper we investigate networks whose evolution is governed by the interaction of a random assembly process and an optimization process. In the first process, new nodes are added one at a time and form connections to randomly selected…
There has been a long debate on how new levels of organization have evolved. It might seem unlikely, as cooperation must prevail over competition. One well-studied example is the emergence of autocatalytic sets, which seem to be a…
Adaptive dynamical networks appear in various real-word systems. One of the simplest phenomenological models for investigating basic properties of adaptive networks is the system of coupled phase oscillators with adaptive couplings. In this…
Heterozygote disadvantage is potentially a potent driver of population genetic divergence. Also referred to as underdominance, this phenomena describes a situation where a genetic heterozygote has a lower overall fitness than either…
A coupled cell system is an ODE system associated with a coupled cell network, where the dimension is determined by the number of cells. A heteroclinic connection is a set of solution trajectories between two equilibria of an ODE system. A…
The mutual influence of dynamics and structure is a central issue in complex systems. In this paper we study by simulation slow evolution of network under the feedback of a local-majority-rule opinion process. If performance-enhancing local…
A central feature of complex systems is the relevance and entanglement of different levels of description. For instance, the dynamics of ecosystems can be alternatively described in terms of large ecological processes and classes of…
Robust heteroclinic cycles are known to change stability in resonance bifurcations, which occur when an algebraic condition on the eigenvalues of the system is satisfied and which typically result in the creation or destruction of a…
According to the competitive exclusion principle, in a finite ecosystem, extinction occurs naturally when two or more species compete for the same resources. An important question that arises is: when coexistence is not possible, which…
Genetic systems with multiple loci can have complex dynamics. For example, mean fitness need not always increase and stable cycling is possible. Here, we study the dynamics of a genetic system inspired by the molecular biology of…
We study a system of dynamical units, each of which shows excitable or oscillatory behavior, depending on the choice of parameters. When we couple these units with repressive bonds, we can control the duration of collective oscillations for…
Systems with the coexistence of different stable attractors are widely exploited in systems biology in order to suitably model the differentiating processes arising in living cells. In order to describe genetic regulatory networks several…
We study experimentally the synchronization patterns in time-delayed directed Boolean networks of excitable systems. We observe a transition in the network dynamics when the refractory time of the individual systems is adjusted. When the…
Oscillations lie at the core of many biological processes, from the cell cycle, to circadian oscillations and developmental processes. Time-keeping mechanisms are essential to enable organisms to adapt to varying conditions in environmental…
Time-discrete dynamical systems on a finite state space have been used with great success to model natural and engineered systems such as biological networks, social networks, and engineered control systems. They have the advantage of being…
Systems of $N$ identical globally coupled phase oscillators can demonstrate a multitude of complex behaviours. Such systems can have chaotic dynamics for $N>4$ when a coupling function is biharmonic. The case $N = 4$ does not possess…
The effect of disturbance on a model ecosystem of sessile and mutually competitive species [Mathiesen et al. Phys. Rev. Lett. 107, 188101 (2011); Mitarai et al. Phys. Rev. E 86, 011929 (2012) ] is studied. The disturbance stochastically…