arXiv subjects

Alexander Kalloniatis

Publications and source records attributed to Alexander Kalloniatis.

10 recordsLinked to original sources

arXiv2026

Stochastic Non-Linear Influence in Synchronisation Dynamics

We propose a mathematical model that represents the influence of an external actor (influencer) on a network of actors (influenced). The model is an adaptation of control systems within the family of formulations inspired by the Kuramoto Model of synchronisation. Capturing influence as a capacity to affect the character or behaviour of another, we study an external node's ability to influence the synchronisation of the Kuramoto system while its global behaviour is pulled to the external node's frequency and away from its natural mean frequency. In our work, stochastically generated dynamical weights assigned to the links between the network and the external influencer whereby links from one system to the other are assigned via one-sided heavy tail noise, generated by the Gamma distribution. We perform numerical experiments to examine transition points in the ability of the external node to alter the behaviour of the influenced network; either to disrupt synchronisation or to drive it to collective frequencies determined by the external node. We examine the dependence of transition points on the external node's frequency, where too ambitious a driving frequency fails to influence the system while retaining a synchronised state, and reducing achieves a state of synchronisation at a frequency shifted from the mean natural frequency. We also look at the analytic approximation for the system close to synchronisation and fragmentation to understand its behaviour around this limit.

math.DS↗

arXiv2023

Calibrating Coupling for Collaboration with Kuramoto

We calibrate a Kuramoto model inspired representation of peer-to-peer collaboration using data on the maximum team-size where coordination breaks down. The Kuramoto model is modified, normalising the coupling by the degree of input and output nodes, reflecting dispersion of cognitive resources in both absorbing incoming-and tracking outgoing-information. We find a critical point, with loss of synchronisation as the number of nodes grows and analytically determine this point and calibrate the coupling with the known maximum team size. We test that against the known `span of control' for a leader/supervisor organisation. Our results suggest larger maximum team sizes than early management science proposes, but are consistent with recent studies.

physics.soc-ph↗

arXiv2023

Mathematical modelling of decision cycles in a competitive environment with neutral parties

Decision making is a human process that is a fundamental part of competition. As a realisation of decision making, Command and Control, or C2, has been studied in the literature for adversarial populations, yet these models do not explicitly capture competition. Our work here seeks to enrich such competition models by extending ecologically inspired population models to include decision dynamics through coupling with a nonlinear system of oscillators (the Kuramoto equation) to model the action-perception cycle in decision making. Through asymmetric competition models of increasing complexity, we highlight the importance of competitive agility and decision making processes necessary for a population to be successful.

math.DS↗

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↗

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↗