How a complex network is connected crucially impacts its dynamics and function. Percolation, the transition to extensive connectedness on gradual addition of links, was long believed to be continuous, but recent numerical evidence of ‘explosive percolation’ suggests that it might also be discontinuous if links compete for addition. Here we analyse the microscopic mechanisms underlying discontin...

We use the concept of the Filippov solution to study the dynamics of a class of delayed dynamical systems with discontinuous right-hand side, which contains the widely studied delayed neural network models with almost periodic self-inhibitions, interconnection weights, and external inputs. We prove that diagonal-dominant conditions can guarantee the existence and uniqueness of an almost periodi...

In this paper, a novel adaptive sliding mode control for rigid robot manipulators is proposed. In the proposed system, since there may exist explicit unknown parameters and perturbations, a Lyapunov based approach is presented to increase system robustness, even in presence of arbitrarily large (but not infinite) discontinuous perturbations. To control and track the robot, a continuous controll...

Submerged breakwaters are one of the shore protective structures. Any discontinuity in these breakwaters causes changes on current parameters including speed and water surface profile. In this paper, discontinuous submerged breakwaters were modelled to investigate the changes in the wave and flow pattern.To investigate the phenomenon, three models including a shore with constant slope, a shore ...

One-dimensional piecewise-smooth discontinuous maps (maps with gaps) are known to have surprisingly rich dynamics, including periodic orbits with very high period and bifurcation diagrams showing period-adding or period-incrementing behavour. In this paper we study a new class of maps, which we refer to as regularised one-dimensional discontinuous maps, because they give very similar dynamics t...

We discuss the Sinai method of proving ergodicity of a discontinuous Hamiltonian system with (non-uniform) hyperbolic behavior.

We discuss the Sinai method of proving ergodicity of a discontinuous Hamiltonian system with (non-uniform) hyperbolic behavior.

This paper is devoted to the study of some nonlinear hyperbolic equations or systems with discontinuous coefficients or with source terms. The common feature of the considered problems is the fact that the jacobian matrix of an associated autonomous system is not diagonalizable in R for many values of the unknown (leading to linear ill posed problems). However, the nonlinear problems appear to ...

The paper presents a new method of performing integrator backstepping in systems that are discontinuous, either due to their inherent structure or because of the applied control input. The proposed technique is applied to the stabilization problem of the dynamic system of a nonholonomic mobile robot. Simulation studies indicate that the methodology can also help alleviate the problem of chatter...