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We study an autocatalytic system consisting of several interacting chemical species. We observe a strong dependence of the concentrations of the chemicals on the size of the system. This dependence is caused by the discrete nature of the…
Coupled dynamical systems with one slow element and many fast elements are analyzed. By averaging over the dynamics of the fast variables, the adiabatic kinetic branch is introduced for the dynamics of the slow variable in the adiabatic…
A wide variety of biological as well as non-biological processes and phenomena involving ion channels, binding, pH, folding/unfolding and effects of chain length are well represented by multiphasic profiles, a series of straight lines…
We investigate the emergence of complex dynamics in a system of coupled dissipative kicked rotors and show that critical transitions can be understood via bifurcations of simple states. We study multistability and bifurcations in the single…
Linear thresholding systems have been used as a model of neural activation and more recently proposed as a model of gene regulation. Here we exhibit linear thresholding systems whose dynamics produce surprisingly long cycles.
Systems with long range interactions display some anomalies when its dynamics and thermodynamics are studied below certain conditions. Among these anomalies are the quasi- stationary states, which are exacerbated because of special initial…
We report in this paper a complete analytical study on the bifurcations and chaotic phenomena observed in certain second-order, non-autonomous, dissipative chaotic systems. One-parameter bifurcation diagrams obtained from the analytical…
Complex systems such as ecosystems, electronic circuits, lasers or chemical reactions can be modelled by dynamical systems which typically experience bifurcations. Transients typically suffer extremely long delays at the vicinity of…
We completely describe the size and large intersection properties of the Holder singularity sets of Levy processes. We also study the set of times at which a given function cannot be a modulus of continuity of a Levy process. The Holder…
We study general aspects of active motion with fluctuations in the speed and the direction of motion in two dimensions. We consider the case in which fluctuations in the speed are not correlated to fluctuations in the direction of motion,…
In this paper, I present a summary on some works that utilized static analysis techniques for understanding biological systems. Control flow analysis, context dependent analysis, and other techniques were employed to investigate the…
Tangencies correspond to singularities of impact systems, separating between impacting and non-impacting trajectory segments. The closure of their orbits constitute the singularity set, which, even in the simpler billiard limit, is known to…
Long-range interacting systems exhibit unusual physical properties not shared by systems with short-range interactions. Understanding the dynamical and statistical effects of long-range interactions yields insights into a host of physical…
This paper is concerned with the analysis of a class of impacting systems of relevance in applications: cam-follower systems. We show that these systems, which can be modelled as discontinuously forced impact oscillators, can exhibit…
A one-dimensional model on a line of the length L is investigated, which involves particle diffusion as well as single particle annihilation. There are also creation and annihilation at the boundaries. The static and dynamical behaviors of…
Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends…
We investigate the occurrence of bifurcations in the dynamical trajectories depicting central nuclear collisions at Fermi energies. The quantitative description of the reaction dynamics is obtained within a new transport model, based on the…
We study systems with periodically oscillating parameters that can give way to complex periodic or non periodic orbits. Performing the long time limit, we can define ergodic averages such as Lyapunov exponents, where a negative maximal…
In piecewise-smooth differential systems, a hyperbolic limit cycle of a subsystem loses its structural stability if it grazes the switching manifold at a tangent point. Such a cycle is called a grazing loop and in this paper we investigate…
Recent microfluidic experiments revealed that large particles advected in a fluidic loop display long-range hydrodynamic interactions. However, the consequences of such couplings on the traffic dynamics in more complex networks remain…