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We introduce and solve a general model of dynamic response under external perturbations. This model captures a wide range of systems out of equilibrium including Ising models of physical systems, social opinions, and population genetics.…

Understanding urban mobility requires models that capture how people interact with and navigate the built environment. We present a scalable, generalizable agent-based framework in which daily schedules emerge from the interplay between…

Fish, birds, insects and robots frequently swim or fly in groups. During their 3 dimensional collective motion, these agents do not stop, they avoid collisions by strong short-range repulsion, and achieve group cohesion by weak long-range…

We present a simple model for describing the dynamics of the interaction between a homogeneous population or society, and the natural resources and reserves that the society needs for its survival. The model is formulated in terms of…

A field deterministic model of the vehicular dynamics in a generic urban street canyon with two neighboring canyons is considered. The assumed hydrodynamical model of vehicular movement is coupled to the gasdynamical model of the air and…

The propagation of traffic congestion along roads is a commonplace nonlinear phenomenon. When many roads are connected in a network, congestion can spill from one road to others as drivers queue to enter a congested road, creating further…

We analyze the stability properties of equilibrium solutions and periodicity of orbits in a two-dimensional dynamical system whose orbits mimic the evolution of the price of an asset and the excess demand for that asset. The construction 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…

Perimeter control is an effective urban traffic management strategy that regulates inflow to congested urban regions using aggregate network dynamics. While existing approaches primarily optimize system-level efficiency, such as total…

We address the issue of the dynamics of wealth accumulation and economic crisis triggered by extreme inequality, attempting to stick to most possibly intrinsic assumptions. Our general framework is that of pure or modified multiplicative…

Urban growth sometimes leads to rigid infrastructure that struggles to adapt to changing demand. This paper introduces a novel approach, aiming to enable cities to evolve and respond more effectively to such dynamic demand. It identifies…

We develop an agent-based model on a lattice to investigate territorial development motivated by markings such as graffiti, generalizing a previously-published model to account for $K$ groups instead of two groups. We then analyze this…

A model of the dynamics of natural rotifer populations is described as a discrete nonlinear map depending on three parameters, which reflect characteristics of the population and environment. Model dynamics and their change by variation of…

For past several decades, research efforts in population modelling has proven its efficacy in understanding the basic information about residential and commercial areas, as well as for the purposes of planning, development and improvement…

We introduce a simple lattice model of traffic flow in a city where drivers optimize their route-selection in time in order to avoid traffic jams, and study its phase structure as a function of the density of vehicles and of the drivers'…

The amount of data that is being gathered about cities is increasing in size and specificity. However, despite this wealth of information, we still have little understanding of what really drives the processes behind urbanisation. In this…

We introduce a novel concept of simple loop dwell time and use it to give sufficient conditions for stability of a continuous-time linear switched system where switching between subsystems is governed by an underlying graph. We present a…

As connected and autonomous vehicles become more widespread, platooning has emerged as a key strategy to improve road capacity, reduce fuel consumption, and enhance traffic flow. However, the benefits of platoons strongly depend on their…

We introduce a simple method to estimate the system parameters in continuous dynamical systems from the time series. In this method, we construct a modified system by introducing some constants (controlling constants) into the given…

Understanding urban dynamics, i.e., how the types and intensity of urban residents' activities in the city change along with time, is of urgent demand for building an efficient and livable city. Nonetheless, this is challenging due to the…