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Sep 2026
Explicit Second-Order Bounds on the Domain of Validity for Lyapunov-Schmidt Reduction
Lyapunov-Schmidt reduction is a widely used dimensionality reduction technique for bifurcation analysis in high-dimensional systems. While classical formulations guarantee the local existence of reduced-order equations, they typically lack explicit quantitative estimates on the size of the neighbourhoods in which these...
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Preprint
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Long-time behavior of McKean--Vlasov stochastic systems with singular coefficients
We develop a quantitative framework for the long-time behavior of McKean--Vlasov stochastic differential equations with singular coefficients and possible phase transitions. The framework separates the existence of invariant measures from their uniqueness. For existence, we introduce a generalized Lyapunov condition wi...
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Open access
Sep 2026
Comparative Study of Constant- and Variable-Order Fractional Dynamics with RBFNN Approximation
The analysis of the complexity of dynamical systems generally presents a major dilemma between including the complexity of memory effects and being computationally efficient. For this purpose, this study proposes an unusual three-dimensional variable-order fractional chaotic system with absolute-value nonlinearity, whi...
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Preprint
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An Efficient Symbolic Algorithm for Computing Lyapunov Constants in Planar Switching Systems
Lyapunov constants are a crucial tool for analyzing bifurcation behavior in switching systems. This paper proposes an efficient algebraic symbolic algorithm for computing Lyapunov constants in planar switching systems. By mapping the vector fields into the complex domain, we construct a normal form algorithm based on L...
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Open access
Aug 2026
Dynamics of a Novel 4D Chaotic System: Stability, Bifurcation, Chaos, and Complexity Analysis for Constant and Variable Fractional Orders
Four-dimensional chaotic systems have garnered significant attention due to their complex nonlinear dynamics, high-dimensional complexity, and wide range of applications in science and engineering. This paper proposes and investigates a novel four-dimensional chaotic system in both constant- and variable-order framewor...
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Open access
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Unveiling and resolving algorithmic false chaos in fractional-order systems via infinite state representation
Lyapunov exponents (LEs) are central to characterizing the long-time dynamics of fractional-order systems (FOS). However, classical discrete reorthonormalization algorithms rely on the semigroup property of integer-order flows. Directly applying these local geometric operations to non-local fractional operators therefo...
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