Analytical and Approximate Methods for Complex Dynamical Systems

Part I: General and specific problems of complex dynamical systems.- Organising centres in a 2D discontinuous map.- Phase models for coupled oscillator networks.- The conflict problem and opinion formation models.- Dynamics of conflict interaction in terms of minimal players.- Generalised intermittency in non-ideal and "classical" dynamical systems.- Lanchester's equations in conflicting sides using ODEINT Python library.- Reversible saddle-node separatrix-loop bifurcation.- Stationary and travelling synchronisation patterns in systems of coupled active rotators.- Part II: Continuum media modelling.- Complex dynamical systems of two-dimensional sloshing in rectangular tank.- Swirling-type sloshing in square base tank due to orbital excitations.- Towards kinetic equations of open systems of active soft matter.- Freely oscillating drop.- Nonlinear WKB method, asymptotic soliton-like solutions of variable coefficients Korteweg-de Vries equations with singular perturbation and Rankine-Hugoniot-type conditions.- Part III: Auxiliary problems of complex dynamical systems.- On group classification of nonlinear heat equation: algebraic approach.- Mathematical modelling of the interconnected boundary-value problems in the Hilbert space.- Averaging in a generalised multifrequency system with a delay.- Exponentially convergent method for Hardy-Titchmarsh-type equation with unbounded operator coefficient in Banach space.- Regularization of linear impulsive boundary value problem for systems of integro-differential equations.- Interconnected system for the Lyapunov equation with control and boundary conditions.- Lyapunov function and smooth periodic solutions to quasilinear 1D hyperbolic systems.