arXiv subjects

Mathew Zuparic

Publications and source records attributed to Mathew Zuparic.

11 recordsLinked to original sources

arXiv2025

Opinion dynamics modelling: distinct attraction and repulsion topologies highlight quantitative effects of trolling

We introduce a model of opinion dynamics based on networked non-linear differential equations. The model combines a linear attraction with a repulsive hyperbolic tangent interaction, labeled controversialness. For low controversialness the model displays universal consensus, which is typical of opinion models. As controversialness increases, opinion behaviours such as polarisation, clustering and dissensus emerge, dependent on the network topology. By placing attractive and repulsive interactions on distinct networks, this model is able to simulate the manipulative effects of trolls by introducing controversy, which may be associated with mis/disinformation, toxic messaging, and encouraging provocative questioning and/or emotional posting. This work offers an analytical and statistical analysis of model results, under a wide variety of topologies and initial conditions, whilst also generalising cluster detection algorithms typically applied to discrete models.

physics.soc-ph↗

arXiv2023

Unifying warfighting functions in mathematical modelling: combat, manoeuvre, and C2

The outcomes of warfare have rarely only been characterised by the quantity and quality of individual combatant force elements. The ability to manoeuvre and adapt across force elements through effective Command and Control (C2) can allow smaller or weaker forces to overcome an adversary with greater resource and fire-power. In this paper, we combine the classic Lanchester combat model with the Kuramoto-Sakaguchi model for phase oscillators on a network to create a flexible Networked-Lanchester-C2 representation of force-on-force military engagement. The mathematical model thus unifies three of the military warfighting `functions': fires, manoeuvre and C2. We consider three illustrative use-cases, and show that an analytical treatment of a reduced model characterises global effects in the full system. For inhomogeneous forces we observe that with appropriate balance between internal organisational coupling, resource manoeuvrability and even weaker lethality the force can be adaptive to overcome an initially stronger adversary.

math.DS↗

arXiv2022

Modelling host population support for combat adversaries

We consider a model of adversarial dynamics consisting of three populations, labelled Blue, Green and Red, which evolve under a system of first order nonlinear differential equations. Red and Blue populations are adversaries and interact via a set of Lanchester combat laws. Green is divided into three sub-populations: Red supporters, Blue supporters and Neutral. Green support for Red and Blue leads to more combat effectiveness for either side. From Green's perspective, if either Red or Blue exceed a size according to the capacity of the local population to facilitate or tolerate, then support for that side diminishes; the corresponding Green population reverts to the neutral sub-population, who do not contribute to combat effectiveness of either side. The mechanism for supporters deciding if either Blue or Red are too big is given by a logistic-type interaction term. The intent of the model is to examine the role of influence in complex adversarial situations typical in counter-insurgency, where victory requires a genuine balance between maintaining combat effectiveness and support from a third party whose backing is not always assured.

math.DS↗

arXiv2021

Optimising structure in a networked Lanchester Model for Fires and Manoeuvre in Warfare

We present a generalisation of the classical Lanchester model for directed fire between two combat forces but now employing networks for the manoeuvre of Blue and Red forces, and the pattern of engagement between the two. The model therefore integrates fires between dispersed elements, as well as manoeuvre through an internal-to-each-side diffusive interaction. We explain the model with several simple examples, including cases where conservation laws hold. We then apply an optimisation approach where, for a fixed-in-structure adversary, we optimise the internal manoeuvre and external engagement structures where the trade-off between maximising damage on the adversary and minimising own-losses can be examined. In the space of combat outcomes this leads to a sequence of transitions from defeat to stalemate and then to victory for the force with optimised networks. Depending on the trade-off between destruction and self-preservation, the optimised networks develop a number of structures including the appearance of so-called sacrificial nodes, that may be interpreted as feints, manoeuvre hubs, and suppressive fires. We discuss these in light of Manoeuvre Warfare theory.

math.OC↗

arXiv2021

Two network Kuramoto-Sakaguchi model under tempered stable Lévy noise

We examine a model of two interacting populations of phase oscillators labelled `Blue' and `Red'. To this we apply tempered stable Lévy noise, a generalisation of Gaussian noise where the heaviness of the tails parametrised by a power law exponent $α$ can be controlled by a tempering parameter $λ$. This system models competitive dynamics, where each population seeks both internal phase synchronisation and a phase advantage with respect to the other population, subject to exogenous stochastic shocks. We study the system from an analytic and numerical point of view to understand how the phase lag values and the shape of the noise distribution can lead to steady or noisy behaviour. Comparing the analytic and numerical studies shows that the bulk behaviour of the system can be effectively described by dynamics in the presence of tilted ratchet potentials. Generally, changes in $α$ away from the Gaussian noise limit, $1< α< 2$, disrupts the locking between Blue and Red, while increasing $λ$ acts to restore it. However we observe that with further decreases of $α$ to small values, $α\ll 1$, with $λ\neq 0$, locking between Blue and Red may be restored. This is seen analytically in a restoration of metastability through the ratchet mechanism, and numerically in transitions between periodic and noisy regions in a fitness landscape using a measure of noise. This non-monotonic transition back to an ordered regime is surprising for a linear variation of a parameter such as the power law exponent and provides a novel mechanism for guiding the collective behaviour of such a complex competitive dynamical system.

cond-mat.stat-mech↗

arXiv2021

Analytic solution to space-fractional Fokker-Planck equations for tempered-stable Lévy distributions with spatially linear, time-dependent drift

We derive analytic solutions for the full time dependence of space-fractional Fokker-Planck equations corresponding to stochastic Langevin equations with additive tempered-stable Lévy noise terms. The drift terms are generalised to be spatially linear, but may contain arbitrary time dependence such that no steady-state solution is available, even for the deterministic system.

cond-mat.stat-mech↗

arXiv2021

Noise driven current reversal and stabilisation in the tilted ratchet potential subject to tempered stable Lévy noise

We consider motion of a particle in a one-dimensional tilted ratchet potential subject to two-sided tempered stable Lévy noise characterised by strength $Ω$, fractional index $α$, skew $θ$ and tempering $λ$. We derive analytic solutions to the corresponding Fokker-Planck Lévy equations for the probability density. Due to the periodicity of the potential, we carry out reduction to a compact domain and solve for the analogue there of steady-state solutions which we represent as wrapped probability density functions. By solving for the expected value of the current associated with the particle motion, we are able to determine threshold for metastability of the system, namely when the particle stabilises in a well of the potential and when the particle is in motion, for example as a consequence of the tilt of the potential. Because the noise may be asymmetric, we examine the relationship between skew of the noise and the tilt of the potential. With tempering, we find two remarkable regimes where the current may be reversed in a direction opposite to the tilt or where the particle may be stabilised in a well in circumstances where deterministically it should flow with the tilt.

cond-mat.stat-mech↗

arXiv2021

Green's functions and the Cauchy problem of the Burgers hierarchy and forced Burgers equation

We consider the Cauchy problem for the Burgers hierarchy with general time dependent coefficients. The closed form for the Green's function of the corresponding linear equation of arbitrary order $N$ is shown to be a sum of generalised hypergeometric functions. For suitably damped initial conditions we plot the time dependence of the Cauchy problem over a range of $N$ values. For $N=1$, we introduce a spatial forcing term. Using connections between the associated second order linear Schrödinger and Fokker-Planck equations, we give closed form expressions for the corresponding Green's functions of the sinked Bessel process with constant drift. We then apply the Green's function to give time dependent profiles for the corresponding forced Burgers Cauchy problem.

nlin.SI↗

arXiv2020

Adversarial decision strategies in multiple network phased oscillators: the Blue-Green-Red Kuramoto-Sakaguchi model

We consider a model of three interacting sets of decision-making agents, labeled Blue, Green and Red, represented as coupled phased oscillators subject to frustrated synchronisation dynamics. The agents are coupled on three networks of differing topologies, with interactions modulated by different cross-population frustrations, internal and cross-network couplings. The intent of the dynamic model is to examine the degree to which two of the groups of decision-makers, Blue and Red, are able to realise a strategy of being ahead of each others' decision-making cycle while internally seeking synchronisation of this process -- all in the context of further interactions with the third population, Green. To enable this analysis, we perform a significant dimensional reduction approximation and stability analysis. We compare this to a numerical solution for a range of internal and cross-network coupling parameters to investigate various synchronisation regimes and critical thresholds. The comparison reveals good agreement for appropriate parameter ranges. Performing parameter sweeps, we reveal that Blue's pursuit of a strategy of staying too-far ahead of Red's decision cycles triggers a second-order effect of the Green population being ahead of Blue's cycles. This behaviour has implications for the dynamics of multiple interacting social groups with both cooperative and competitive processes.

nlin.AO↗

arXiv2020

Information theory and player archetype choice in Hearthstone

Using three years of game data of the online collectible card game Hearthstone, we analyse the evolution of the game's system over the period 2016--2019. By considering the frequencies that archetypes are played, and their corresponding win-rates, we are able to provide narratives of the system-wide changes that have occurred over time, and player reactions to them. Applying the archetype frequencies to analyse the system's Shannon entropy, we characterise the salient features of the time series of player choice. Paying particular attention to how entropy is affected during periods of both small and large-scale change, we are able to demonstrate the effects of increased player experimentation before popular decks and tactics emerge. Furthermore, constructing conditional probabilities that simulate understandable player behaviour, we analyse the system's information storage and test the explain-ability of current player choice based on previous decision-making.

nlin.AO↗

arXiv2013

Stochastic (in)stability of synchronisation of oscillators on networks

We consider the influence of correlated noise on the stability of synchronisation of oscillators on a general network using the Kuramoto model for coupled phases $θ_i$. Near the fixed point $θ_i \approx θ_j \ \forall i,j$ the impact of the noise is analysed through the Fokker-Planck equation. We deem the stochastic system to be `weakly unstable' if the Mean First Passage Time for the system to drift outside the fixed point basin of attraction is less than the time for which the noise is sustained. We argue that a Mean First Passage Time, computed near the phase synchronised fixed point, gives a useful lower bound on the tolerance of the system to noise. Applying the saddle point approximation, we analytically derive general thresholds for the noise parameters for weak stochastic stability. We illustrate this by numerically solving the full Kuramoto model in the presence of noise for an example complex network.

cond-mat.stat-mech↗