Related papers: Replicator dynamical systems and their gradient an…
Evolutionary game theory has impacted many fields of research by providing a mathematical framework for studying the evolution and maintenance of social and moral behaviors. This success is owed in large part to the demonstration that the…
Lyapunov exponents are well-known characteristic numbers that describe growth rates of perturbations applied to a trajectory of a dynamical system in different state space directions. Covariant (or characteristic) Lyapunov vectors indicate…
When neural networks are used to model dynamics, properties such as stability of the dynamics are generally not guaranteed. In contrast, there is a recent method for learning the dynamics of autonomous systems that guarantees global…
We show that a number of models in virus dynamics, epidemiology and plant biology can be presented as ``damped" versions of the Lotka-Volterra predator-prey model, by analogy to the damped harmonic oscillator. The analogy deepens with the…
The replicator equations are a family of ordinary differential equations that arise in evolutionary game theory, and are closely related to Lotka-Volterra. We produce an infinite family of replicator equations which are Liouville-Arnold…
Evolutionary game dynamics is one of the most fruitful frameworks for studying evolution in different disciplines, from Biology to Economics. Within this context, the approach of choice for many researchers is the so-called replicator…
Generic dynamical systems have `typical' Lyapunov exponents, measuring the sensitivity to small perturbations of almost all trajectories. A generic system has also trajectories with exceptional values of the exponents, corresponding to…
Imitation learning algorithms can be used to learn a policy from expert demonstrations without access to a reward signal. However, most existing approaches are not applicable in multi-agent settings due to the existence of multiple (Nash)…
We present a general approach to the classical dynamical systems simulation. This approach is based on classical systems extension to quantum states. The proposed theory can be applied to analysis of multiple (including non-Hamiltonian)…
Multi-agent interacting systems are prevalent in the world, from pure physical systems to complicated social dynamic systems. In many applications, effective understanding of the situation and accurate trajectory prediction of interactive…
We consider generalized linear stochastic dynamical systems with second-order state transition matrices. The entries of the matrix are assumed to be either independent and exponentially distributed or equal to zero. We give an overview of…
We introduce static and dynamic correlation functions for the spatial densities of Lyapunov vector fluctuations. They enable us to show, for the first time, the existence of hydrodynamic Lyapunov modes in chaotic many-particle systems with…
Understanding the emergence and stability of cooperation in public goods games is important due to its applications in fields such as biology, economics, and social science. However, a gap remains in comprehending how mutations, both…
The correspondence between a high-order non symmetric difference operator with complex coefficients and the evolution of an operator defined by a Lax pair is established. The solution of the discrete dynamical system is studied, giving…
The dynamics of protection processes has been a fundamental challenge in systemic risk analysis. The conceptual principle and methodological techniques behind the mechanisms involved [in such dynamics] have been harder to grasp than…
The evolution of specialization in a multi-agent system is studied both by computer simulation and Markov process model. Many individual agents search for and exploit resources to get global optimization in an environment without complete…
We study games in which the set of strategies is multi-dimensional, and new agents might learn various strategic dimensions from different mentors. We introduce a new family of dynamics, the recombinator dynamics, which is characterised by…
Stability and analysis of multi-agent network systems with state-dependent switching typologies have been a fundamental and longstanding challenge in control, social sciences, and many other related fields. These already complex systems…
For over fifty years, the dynamical systems perspective has had a prominent role in evolutionary biology and economics, through the lens of game theory. In particular, the study of replicator differential equations on the standard…
Multiagent systems aim to accomplish highly complex learning tasks through decentralised consensus seeking dynamics and their use has garnered a great deal of attention in the signal processing and computational intelligence societies. This…