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We study the oscillatory dynamics in the generic three-species rock-paper-scissors games with mutations. In the mean-field limit, different behaviors are found: (a) for high mutation rate, there is a stable interior fixed point with…
This paper examines the oscillatory behaviour of complex viscoelastic systems with power law-like relaxation behaviour. Specifically, we use the fractional Maxwell model, consisting of a spring and fractional dashpot in series, which…
Transit surveys have revealed a significant population of compact multi-planet systems, containing several sub-Neptune-mass planets on close-in, tightly-packed orbits. These systems are thought to have formed through a final phase of giant…
Critical transitions or regime shifts are sudden and unexpected changes in the state of an ecosystem, that are usually associated with dangerous levels of environmental change. However, recent studies show that critical transitions can also…
Theoretical models that describe oscillations in biological systems are often either a limit cycle oscillator, where the deterministic nonlinear dynamics gives sustained periodic oscillations, or a noise-induced oscillator, where a fixed…
We explore the dynamics of hard-core lattice bosons in the presence of strong non-local particle loss. The evolution occurs on two distinct time-scales, first a rapid strongly correlated decay into a highly degenerate Zeno state subspace,…
Oscillators have two main limitations: their synchronization properties are limited (i.e they have a finite synchronization region) and they have no memory of past interactions (i.e. they return to their intrinsic frequency whenever the…
We provide an introduction to infinite-dimensional port-Hamiltonian systems. As this research field is quite rich, we restrict ourselves to the class of infinite-dimensional linear port-Hamiltonian systems on a one-dimensional spatial…
We study the dynamics and the resulting state after relaxation in a quasi-disordered integrable lattice system after a sudden quench. Specifically, we consider hard-core bosons in an isolated one-dimensional geometry in the presence of a…
This work aims at understanding the slow dynamics of a nonlocal fast-slow stochastic evolutionary system with stable Levy noise. Slow manifolds along with exponential tracking property for a nonlocal fast-slow stochastic evolutionary system…
We propose and study a one-dimensional $2\times 2$ hyperbolic Eulerian system with local relaxation from critical threshold phenomena perspective. The system features dynamic transition between strictly and weakly hyperbolic. For different…
We consider the Ising model on a small-world network, where the long-range interaction strength $J_2$ is in general different from the local interaction strength $J_1$, and examine its relaxation behaviors as well as phase transitions. As…
We demonstrate thermo-mechanical relaxation oscillations in a strongly driven quartz crystal. Dynamic bifurcation leads to two stable oscillation states with a distinct electrical impedance. Slow Joule-heating, which shifts the…
Stochastic systems characterised by a random driving in a form of the general stable noise are considered. The particle experiences long rests due to the traps the density of which is position-dependent and obeys a power-law form attributed…
We consider the rates of noise-induced switching between the stable states of dissipative dynamical systems with delay and also the rates of noise-induced extinction, where such systems model population dynamics. We study a class of systems…
The goal of this paper is to study the Moderate Deviation Principle (MDP) for a system of stochastic reaction-diffusion equations with a time-scale separation in slow and fast components and small noise in the slow component. Based on weak…
The nonexponential relaxation ocurring in complex dynamics manifested in a wide variety of systems is analyzed through a simple model of diffusion in phase space. It is found that the inability of the system to find its equilibrium state in…
Recent developments in data-driven control have revived interest in the behavioral approach to systems theory, where systems are defined as sets of trajectories rather than being described by a specific model or representation. However,…
We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…
We consider coupled slow-fast stochastic processes, where the averaged slow motion is given by a two-dimensional Hamiltonian system with multiple critical points. On a proper time scale, the evolution of the first integral converges to a…