Dynamical Modeling of Emotions in Complex Systems

Dynamical modelling of emotions applies principles from nonlinear dynamics, network science and affective psychology to characterise how emotional states evolve and interact across individuals and groups. By representing feelings as variables in coupled differential or difference equations, these models capture feedback loops, adaptation and memory effects that underlie mood fluctuations and interpersonal influences. Continuous‐time and discrete‐time formulations have been used to study stability landscapes, bifurcation phenomena and transitions between equilibrium and chaotic attractors. Fractional‐order dynamics extend classical approaches by incorporating long‐term memory kernels, revealing how past experiences modulate present affect. In parallel, stochastic extensions introduce noise and uncertainty to account for individual heterogeneity and external perturbations. Applications range from predicting mood trajectories in clinical populations and simulating sentiment contagion in social networks to optimising intervention policies for relationship maintenance. Key challenges include accurate parameter estimation from limited data, integration of multiscale interactions and validation against empirical time series. Emerging directions emphasise hybrid data‐driven and theory‐driven frameworks, embedding machine learning within principled dynamical systems to enhance predictive precision and interpretability.

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Dynamical Modeling of Emotions in Complex Systems publication trend

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Technical terms

Dynamical system: A mathematical construct in which state variables evolve over time according to deterministic or stochastic laws, often expressed as differential or difference equations.

Fractional‐order dynamics: An extension of classical calculus employing non‐integer derivatives to model memory effects and hereditary properties in dynamic processes.

Bifurcation: A qualitative change in the structure of a system’s solutions that occurs when a parameter crosses a critical threshold, leading to new equilibrium or periodic behaviours.

Lyapunov exponent: A quantitative measure of the average rate at which nearby trajectories diverge or converge, used to assess the presence of chaotic dynamics.

Markov chain: A stochastic model describing a sequence of possible states in which the probability of each state depends only on the preceding one, enabling discrete‐stage analysis of random processes.

Optimal control theory: A mathematical framework for determining control policies that optimise a performance criterion subject to dynamic constraints, widely applied to sustain desired emotional trajectories.

References

1. Chaotic Dynamics of the Fractional-Love Model with an External Environment. Entropy (2018).
2. Discrete mathematical modeling and optimal control of the marital status: the monogamous marriage case. Advances in Continuous and Discrete Models (2017).
3. Statistical Model of College Students’ Mental Health Based on the Law of Large Numbers. Applied Mathematics and Nonlinear Sciences (2023).