Publications by Max-Olivier Hongler

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Today's supply networks consist of a certain amount of logistics objects that are enabled to interact with each other and to decide autonomously upon their next steps: in other words, they exhibit a certain degree of autonomous cooperation. Therefore, modern logistics research regards them as complex adaptive logistics systems. In order to analyze evolving dynamics and underlying implications for the respective systems' behavior as well as the potential outcomes resulting from the interaction between autono

The collective behaviour of stochastic multi-agents swarms driven by Gaussian and non-Gaussian environments is analytically discussed in a mean-field approach. We first exogenously implement long range mutual interactions rules with strengths that are weig ...

The inherent complexity characterizing the production and/or service networks strongly favors decentralized and self-organizing mechanisms to regulate the flows of matter and information in circulation. This basic observation motivates us to study the flow ...

We consider the dynamics of swarms of scalar Brownian agents subject to local imitation mechanisms implemented using mutual rank-based interactions. For appropriate values of the underlying control parameters, the swarm propagates tightly and the distances ...

We derive the behavior of the average exit time (i.e., the number of reflections before escape) of a ray path traveling between two perfect mirrors subject to dynamic random-tilt aberrations. Our calculation is performed in the paraxial approximation. When small random tilts are taken into account, we may consider an asymptotic regime that generically reduces the problem to the study of the exit time from an interval for a harmonic, frictionless oscillator driven by Gaussian white noise. Despite its apparen

We develop an exchange rate target zone model with finite exit time and non-Gaussian tails. We show how the tails are a consequence of time-varying investor risk aversion, which generates mean-preserving spreads in the fundamental distribution. We solve ex ...

By continuously scanning a femtosecond laser beam across a fused silica specimen, we demonstrate the formation of self-organized bubbles buried in the material. Rather than using high intensity pulses and high numerical aperture to induce explosions in the ...

We construct a class of stochastic differential equations driven by white Gaussian noise sources whose solutions can be drawn from skewed Gaussian probability laws, here referred to as skew-Normal diffusion (SKN) processes. The non-Gaussian nature of such processes results from introducing a nonlinear and time-inhomogeneous drift constructed via ad-hoc changes of probability measure (Doob’s h -transform). SKN processes fit naturally within the statistical mechanics of trajectories as they are the driven pro

We consider a network of N coupled limit cycle oscillators, each having a set of control parameters Λ_k, k = 1, . . . , N, that controls the frequency and the geometry of the limit cycle. We implement a self-adaptive mechanism that drives the local systems ...

The fundamental idea that synchronized patterns emerge in networks of interacting oscillators is revisited by allowing a parametric learning mechanism to operate on the local dynamics. The local dynamics consist of stable limit cycle oscillators which, due to mutual interactions, are allowed, via an adaptive process, to permanently modify their frequencies. Adaptivity is made possible by conferring to each oscillator’s frequency the status of an additional degree of freedom. The network of individual oscill

We consider a collection {O_k}_{k=1}^N of interacting parametric mixed canonical-dissipative systems, (MCD). Each individual Ok, exhibits, in absence of interaction, a limit cycle L_k on which the orbit circulation is parameterized by w_k(t). The underlyin ...

he concept of ranked order probability distribution unveils natural probabilistic interpretations for the kink waves (and hence the solitons) solving higher order dispersive Burgers’ type PDEs. Thanks to this underlying structure, it is possible to propose ...

We study some linear and nonlinear shot noise models where the jumps are drawn from a compound Poisson process with jump sizes following an Erlang-m distribution. We show that the associated Master equation can be written as a spatial mth order partial dif ...

We analytically discuss a multiplicative noise generalization of the Kuramoto- Sakaguchi dynamics for an assembly of globally coupled phase oscillators. In the mean-ﬁeld limit, the resulting class of invariant measures coincides with a generalized, two-par ...

In this paper, we present a distributed control strategy, enabling agents to converge onto and travel along a consensually selected curve among a class of closed planar curves. Individual agents identify the number of neighbors within a finite circular sen ...

Beliefs inform the behaviour of forward-thinking agents in complex environments. Recently, sequential Bayesian inference has emerged as a mechanism to study belief formation among agents adapting to dynamical conditions. However, we lack critical theory to ...

We study a collection of limit cycle oscillators with different frequencies interacting via networks. With static networks, our specific class of models produces a frequency learning mechanism leading the collection of oscillators to ultimately adopt a sin ...

We consider a complex network of N diffusively coupled stable limit cycle oscillators. Each individual system has its own set of local parameters Λ, characterizing its frequencies and the shape of limit cycle. The Λ are allowed, thanks to appropriate interactions, to self-adapt. The self-adaptive mechanism ultimately drive all oscillators to a consensual dynamical state where all local systems share a common and constant consensual set of parameters Λ. Interactions are implemented via a coupling matrix whos

The cooperative dynamics of a 1-D collection of Markov jump, interacting stochastic processes is studied via a mean-field (MF) approach. In the time-asymptotic regime, the resulting nonlinear master equation is analytically solved. The nonlinearity compens ...

Among the rich collection of noise sources that can be used to drive stochastic differential equations (SDE), we here focus on Markov processes that themselves are functions of the standard Brownian motion and of the Telegrapher’s process. Our present noise sources can be viewed as lumped versions of Markov processes with enlarged states spaces. The resulting Markov processes exhibit ballistic non-Gaussian noise features with long time range correlations. When used as simple additive noise sources in SDEs,

Max-Olivier Hongler

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Centralized versus decentralized control - A solvable stylized model in transportation

Mean-Field Games And Swarms Dynamics In Gaussian And Non-Gaussian Environments

Circulation of Autonomous Agents in Production and Service Networks

Intearcting Brownian Swarms: Some Analytical Results

Resonator stability subject to dynamic random-tilt aberration

Can one hear the shape of a target zone?

Femtosecond-laser generation of self-organized bubble patterns in fused silica

Skew-Normal Diffusions

Self-Adaptive Attractor-Shaping for Oscillators Networks

Networks of limit cycle oscillators with parametric learning capability

Networks of Mixed Canonic-Dissipative Systems and Dynamic Hebbian Learning

Brownian Swarm Dynamics and Burgers’ Equation with Higher Order Dispersion

On Jump-Diffusive Driving Noise Sources: Some Explicit Results and Applications

Hyperbolic angular statistics for globally coupled oscillators

Decentralized Self-Selection of Swarm Trajectories: From Dynamical Systems to Robotic Implementation

Stochastic pairwise preference convergence in Bayesian agents

Parametric Resonance in Time-Dependent Networks of Hopf Oscillators

Self-shaping attractors for coupled limit cycle oscillators

Exact soliton-like probability measures for interacting jump processes

On Stochastic Processes Driven by Ballistic Noise Sources