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The advent of asteroseismology as the golden path to precisely characterize single stars naturally led to synergies with the field of exoplanetology. Today, the precise determination of stellar masses, radii and ages for exoplanet-host…
We study the dynamics of a second-order difference equation that is derived from a planar Ricker model of two-stage (e.g. adult, juvenile) biological populations. We obtain sufficient conditions for global convergence to zero in the…
The motion of two planets around a Sun-like star under the combined effects of mutual interaction and tidal dissipation is investigated. The secular behaviour of the system is analyzed using two different approaches. First, we solve the…
Epidemic data show the existence of a region of quasi-linear growth (strolling period) of infected cases extending in between waves. We demonstrate that this constitutes evidence for the existence of near time-scale invariance that is…
Corals are the primary habitat-building life-form on reefs that support a quarter of the species in the ocean. A coral reef ecosystem usually consists of reefs, each of which is like a tall building in any city. These reef-building corals…
In this paper we study collective decision making on a multi-population, represented by a regular network of groups of individuals. Each group consists of a collection of players and every player can choose between two options. A group is…
Bifurcation cascades in conservative systems are shown to exhibit a generalized diagram, which contains all relevant informations regarding the location of periodic orbits (resonances), their width (island size), irrational tori and the…
The existence of positive equilibrium solutions to age-dependent population equations with nonlinear diffusion is studied in an abstract setting. By introducing a bifurcation parameter measuring the intensity of the fertility it is shown…
We present an analytical proof assisted by computer calculations for the dynamical stability of the eight main planets and Pluto for the next 100,000 years. It means that the semi-major axes of the planets will not change significantly…
Direct imaging searches have begun to detect planetary and brown dwarf companions and to place constraints on the presence of giant planets at large separations from their host star. This work helps to motivate such planet searches by…
We present a rapid binary evolution algorithm that enables modelling of even the most complex binary systems. In addition to all aspects of single star evolution, features such as mass transfer, mass accretion, common-envelope evolution,…
We present a computer assisted proof or diffusion in the Planar Elliptic Restricted Three Body Problem. We treat the elliptic problem as a perturbation of the circular problem, where the perturbation parameter is the eccentricity of the…
We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we…
We investigate an epidemiological model that incorporates waning of immunity at the individual level and boosting of the immune system upon re-exposure to the pathogen. When immunity is fully restored upon boosting, the system can be…
We study the stability of non-conservative deterministic cross diffusion models and prove that they are approximated by stochastic population models when the populations become locally large. In this model, the individuals of two species…
We investigate the competition between barrier slowing down and proliferation induced superdiffusion in a model of population dynamics in a random force field. Numerical results in $d=1$ suggest that a new intermediate diffusion behaviour…
The dynamics of complex-valued fractional-order neuronal networks are investigated, focusing on stability, instability and Hopf bifurcations. Sufficient conditions for the asymptotic stability and instability of a steady state of the…
In this work, we study the continuation of a periodic orbit on a relatively large scale and discover the existence of convergence under certain conditions, which has profound significance in research on asteroids and can provide a total…
We investigate the structure and stability of the steady states for a bacterial colony model with density-suppressed motility. We treat the growth rate of bacteria as a bifurcation parameter to explore the local and global structure of the…
This paper studies a two microbial species model in competition for a single resource in the chemostat including general interspecific density-dependent growth rates with distinct removal rates for each species. We give the necessary and…