Keywordsouter synchronization; fractional-order derivative; complex network; observer control; LMI; fractional-order systems; parameter identification; genetic algorithm; output error; noise; excitation; system thermodynamics; energy flow; interconnected systems; entropy; Helmholtz free energy; Gibbs free energy; chemical thermodynamics; mass action kinetics; chemical potential; neuroscience and thermodynamics; non-autonomous dynamical systems; switching systems; set-valued pullback attractors; topological entropy; complexity; energy-time coordinates; energy-time eigenfunctions; time in classical systems; time in quantum systems; commutators in classical systems; commutators; diffusive predator-prey system; Leslie-Gower; Holling type III schemes; refuge; stability; pattern formation; topological dynamical system; perfect mapping; co-compact open cover; topological entropy; topological conjugation; Lebesgue number; topological entropy; non-autonomous discrete systems; skew-product; Bowen's inequalities; encrypt; watermark; logistic map; Arnold’s cat map; synchronization; fractional-order; chaotic neural networks; linear feedback control; information entropy; thermodynamic entropy; emergence; chaos; fractal; complexity theory; multiscale analysis; large-scale binary integer programs; linear quadratic tracking; optimal control; combination synchronization; Lyapunov stability theory; complex hyperchaotic Lorenz system; complex hyperchaotic Chen system; complex hyperchaotic L¨u system; seismic events; mutual information; clustering; visualization; generalized entropy; scalar, vector, and matrix cases; optimization; mathematical and statistical models; pathway model; non-extensive statistical mechanics; solar neutrino data; diffusion entropy analysis; standard deviation analysis; Injection pulling; analog frequency dividers; injection-locked frequency dividers (ILFDs); nonlinear oscillators; synchronization; averaging method; energy-time coordinates; energy-time eigenfunctions; time in classical systems; time in quantum systems; harmonic oscillator; linear potential; fractional calculus; non-Fourier heat conduction; fractional diffusion-wave equation; perfect thermal contact; Laplace transform; Mittag-Leffler function; Wright function; Mainardi function; incremental learning; adaptation plot; multiscale; learning entropy; individual sample learning entropy; approximate learning entropy; order of learning entropy; learning entropy of a model; non-Shannon entropy; novelty detection; chaos; time series; HRV; ECG; fractional calculus; fractional differential equations; fractional polynomial neural network; fractional-order dynamical system; fractional dynamics; fractional calculus; fractional-order differential equation; entropy; constant phase element; analogue realization; structural complexity; numerical combination; vertex degree; class; networks; relaxation to fixed points; dissipative mapping; complex system; cubic map; logistic map; synchronization; finite-time stability; hyperchaotic system; complex variable; n-scroll attractor; fractional dynamics; fractional-derivative models; scale; homogeneous; Fractional power series; Caputo fractional derivative; fractional differential equations; multi-objective particle swarm optimization; Shannon entropy; diversity; generalized function projective synchronization; switched state; hyperchaotic system; stability; multiple solutions; fractional differential equations; power series; fractional calculus; entropy; stability; predictability; dynamic systems; football; performance analysis; variability; fractional-order chaotic system; adaptive sliding mode control; input nonlinearity; unknown bounded uncertainties; solar neutrinos; Super-Kamiokande; data analysis; standard deviation; diffusion entropy; entropic pathway model, fractional reaction; fractional diffusion; thermonuclear functions; bifurcation theory; nonsmooth bifurcations; piecewise-smooth systems; limit cycles; topological equivalence; finite-time; chaos; PMSM; Lyapunov stability theory
