arXiv subjects

Vinesh Vijayan

Publications and source records attributed to Vinesh Vijayan.

14 recordsLinked to original sources

arXiv2026

Geometry Induced Adaptive Dissipation in Non Linear Contact Hamiltonian Systems Theory and Application to Duffing Oscillator

We develop a generalized contact Hamiltonian framework by extending canonical contact Hamiltonian mechanics to nonlinear dissipative systems through the replacement of the classical linear contact potential with a smooth nonlinear contact potential. The proposed formulation establishes a generalized energy dissipation law together with a structural characterization of admissible contact-induced damping, introducing effective contact dissipation as an intrinsic geometric measure of adaptive dissipation. As an application, a generalized contact Duffing oscillator is derived, in which dissipation emerges intrinsically from the contact geometry rather than being introduced phenomenologically. Numerical investigations of the generalized contact Duffing oscillator demonstrate that nonlinear contact geometry governs the effective dissipation and produces significant changes in the phase-space structure, energy decay, dynamical stability, and long-term nonlinear behavior. The proposed theory therefore provides a systematic geometric framework for constructing and analyzing nonlinear dissipative Hamiltonian systems within contact Hamiltonian mechanics.

nlin.CD↗

arXiv2026

Complexity Condensation Through Adaptive Information Exchange

An emergent complexity field governing information exchange is the central theme of this work. To explore this idea, we propose a model of an adaptive dynamical network in which both the interaction weights and the adaptive coupling strengths are determined by finite-time information production rates that quantify the dynamical complexity of individual subsystems. Collective organization in complexity space emerges through a feedback mechanism between the microscopic dynamics and the resulting complexity-dependent interactions. Using numerical simulations, we demonstrate the emergence of a phenomenon that we term \emph{complexity condensation}, in which subsystem complexities become strongly localized despite the absence of complete state synchronization. The degree of condensation is found to be maximal at an intermediate adaptation strength, reflecting a balance between selective information exchange and network fragmentation. These results reveal a mechanism for complexity-mediated self-organization in nonlinear systems driven by adaptive information exchange.

nlin.AO↗

arXiv2026

Parametric Modulation of Nonlinear Coupling in the H\'enon Heiles System: Resonances, Chaos, and Stabilization

We investigate parametric modulation of the nonlinear coupling in the Henon Heiles system, which directly modifies intrinsic resonance structure in a manner complementary to additive forcing. Canonical perturbation theory in extended phase space yields normal forms predicting resonance tongues scaling as $\sqrt{\varepsilon}$ near commensurate frequencies. Melnikov analysis quantifies separatrix splitting and chaos onset, confirmed by symplectic simulations showing transition from localized resonances to global transport via overlap. High-frequency averaging reveals potential stiffening that suppresses chaos. parametric modulation of nonlinear coupling provides an alternative route for generating combination resonances and influencing chaotic dynamics

nlin.CD↗

arXiv2026

Breakdown of Linear Response in Uniformly Hyperbolic Systems with Hierarchical Structure

Linear response theory asserts that sufficiently small external biases produce currents proportional to the applied force and forms the theoretical foundation of nonequilibrium transport. Here we demonstrate that linear response can break down even in uniformly hyperbolic deterministic systems when hierarchical asymmetry is present. Using a minimal class of uniformly expanding chaotic maps with hierarchical multiscale structure, we show that progressively finer transport channels become dynamically active as the applied bias decreases. The resulting force current relation is monotone and exhibits a hierarchical, fractal-like organization of activation thresholds. As a consequence, the effective mobility diverges as F to 0, demonstrating breakdown of linear response despite strong chaos and uniform hyperbolicity. The effect arises from deterministic multiscale activation rather than intermittency, stochastic noise, or singular invariant measures. These results identify hierarchy as an independent deterministic mechanism for nonperturbative transport response and demonstrate that uniform hyperbolicity alone does not guarantee the validity of linear response.

nlin.CD↗

arXiv2026

Finite-scale geometric invariants for chaotic and weakly chaotic dynamics

We introduce a finite scale geometric observable that quantifies the growth rate of localized sets under time evolution in dissipative dynamical systems. Defined at finite time and resolution without reference to symbolic dynamics or Markov partitions this observable converges, in uniformly hyperbolic systems, to a resolution dependent plateau whose logarithmic scaling coefficient equals the Kolmogorov Sinai entropy. In merely hyperbolic systems, it decays to zero, reflecting the absence of entropy production, while remaining well defined at finite scales. Numerical results for the Henon map and Feigenbaum point illustrate these behaviors. Our findings yield a finite scale geometric characterization of chaotic dynamics, consistent with classical entropy theory where applicable. We further demonstrate that the observable remains well defined in open intermittent systems, where trajectories escape and classical asymptotic invariants fail, revealing finite scale signatures of transient weak chaos.

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arXiv2025

Universality classes of chaos in non Markovian dynamics

Classical chaos theory rests on the notion of universality, whereby disparate dynamical systems share identical scaling laws. Existing universality classes, however, implicitly assume Markovian dynamics. Here, a logistic map endowed with power law memory is used to show that Feigenbaum universality breaks down when temporal correlations decay sufficiently slowly. A critical memory exponent is identified that separates perturbative and memory dominated regimes, demonstrating that long range memory acts as a relevant renormalisation operator and generates a new universality class of chaotic dynamics. The onset of chaos is accompanied by fractional scaling of Lyapunov exponents, in quantitative agreement with analytical predictions. These results establish temporal correlations as a previously unexplored axis of universality in chaotic systems, with implications for physical, biological and geophysical settings where memory effects are intrinsic.

nlin.CD↗

arXiv2025

Geometric Formulation of Combined Conservative Dissipative Mechanics via Contact Hamiltonian Dynamics Symmetries, Reduction, and Variational Integrators

We develop a unified geometric framework for mechanical systems that combine conservative and dissipative dynamics by formulating them on contact manifolds. Within this setting, we identify the Reeb vector field as the intrinsic generator of irreversibility and derive explicit laws describing how dissipation modifies symmetry reduction and momentum evolution. As a concrete application, we construct the contact Hamiltonian formulation of the rigid body with isotropic and anisotropic damping, classify all equilibrium configurations, and analyze their stability. Building on this continuous formulation, we design a second-order structure preserving contact variational integrator obtained by a symmetric splitting of kinetic, potential, and dissipative components. Numerical experiments for representative dissipative systems demonstrate accurate energy decay, geometric consistency, and recovery of the symplectic Verlet scheme in the conservative limit. The proposed framework provides a coherent connection between the geometry of contact dynamics, physical irreversibility, and numerically stable integration, offering new tools for the analysis of mixed conservative dissipative mechanical systems.

math-ph↗

arXiv2025

Universal Curvature Force on Dislocations from a Cartan Geometric Defect Action

We develop a unified Cartan geometric framework where dislocations and disclinations correspond to torsion and curvature of the material coframe connection, respectively, and phase defects emerge as U(1) vortices. This single action principle produces coupled equations of motion and conservation laws governing these defects. Our theory predicts a universal Magnus-like force exerted by curvature on moving dislocations, as well as disclination-driven reconnection events. These phenomena offer experimentally testable signatures in colloidal crystals and mechanical metamaterials.

math-ph↗

arXiv2025

Noise Reinstates Collapsed Populations: Stochastic Reversal of Deterministic Extinction

Conventional wisdom suggests that environmental noise drives populations toward extinction. In contrast, we report a paradoxical phenomenon in which stochasticity reverses a deterministic tipping point, thereby preventing collapse. Using a hybrid model that integrates logistic growth with a density-triggered sigmoidal collapse, we uncover a striking reversal: deterministic fragility on one side, and stochastic rescue under weak noise on the other. Our analysis demonstrates that noise disrupts the convergence of deterministic trajectories toward extinction by altering the phase space topology, enabling back-transitions to viable states. This mechanism gives rise to noise-induced metastability and reveals a form of stochastic robustness not captured by deterministic models. These findings suggest that natural fluctuations can serve as a stabilizing force in complex systems, offering a compelling counter-narrative to classical models in ecology, epidemiology, and beyond. We advocate for a re-evaluation of stabilization strategies, emphasizing the constructive role of stochasticity in averting population collapse.

q-bio.PE↗

arXiv2025

From Disorder to Design: Entropy-Driven Self-Organization in an Agent Based Swarming Model and Pattern Formation

This letter seeks to illuminate the profound connection between complexity, self-organization, emergent behaviour, pattern formation, and entropy concepts that are foundational to understanding our universe. By examining these ideas through the lenses of physics, information theory, and nonlinear dynamics, we uncover a fascinating narrative. Starting with a random cluster of particles possessing distinct internal properties, we activate their interactions and observe the emergence of intricate patterns over time. This journey reveals a transition from unlikely to more probable states. At extreme parameter values, the system showcases stunning patterns and turbulent motions remarkable emergent behaviour propelled by entropy and the dynamic exchange of mutual information. Engaging with probability theory helps us to unveil this intricate connectivity, demonstrating not only its significance but also its potential to reshape our understanding of complex systems.

nlin.AO↗

arXiv2022

Cyclically Symmetric Thomas Oscillators As Swarmalators : A paradigm for Active Fluids & Pattern Formation

In this letter, we demonstrate the cyclically symmetric Thomas oscillators as swarmalators and describe their possible collective dynamics. We achieve this by sewing Kuromoto-type phase dynamics to particle dynamics represented by the Thomas model. More precisely, this is equivalent to a non-linear particle aggregation model with cyclic symmetry of coordinates and position-dependent phase dynamics. The non-linear equations describe spatiotemporal patterns of crystalline order and chaotic randomness at two extreme values of the system parameter. This pattern is the outcome of non-linear self-organization, which leads to a new class of turbulent flow - active turbulence. We claim that this model can capture the dynamics of many naturally occurring microorganisms and micro-swimmers. The model described in this letter can be a prototypical model for understanding active systems and may shed light on the possibility of making novel materials(active matter) with exciting biomedical and industrial applications. The key to this is the understanding and control over the complex dynamics of active systems, an out-of-equilibrium system, which is potentially helpful in making functional materials, nano and micromachines.

nlin.AO↗

arXiv2022

Collective motion of mutually coupled Thomas Oscillators: Spatially Separated Swirling Motion and Eddy Diffusion

In this letter, we report a numerical study on the collective dynamics of two mutually coupled Thomas oscillators with linear/nonlinear coupling in a dynamic environment. We claim our model calculations can explain the diffusion of interacting particles in a fluid. In an ordinary fluid, frequent momentum transfer between particles keeps the particles in a fluid moving together with correlated time behaviour. The diffusion of interacting particles in a dynamic environment like this is a nonequilibrium phenomenon and is similar to the observed transient chaotic dynamics in the model. The detailed study of the nature of dynamics and synchronization reveals that, for two qualitatively different regimes of system parameters, the coupled system passes through an interval of transient chaos before it settles into a chaotic or limit cycle attractor. The linear diffusive coupling is equivalent to weak momentum transfer, leading to conventional dynamics and synchronization. The sinusoidal nonlinear coupling, harmonic momentum transfer, produces exceptional dynamical features. The nature of synchronization is complete(directed motion) when the attractor is chaotic or an unstable transient attractor. In contrast, it is either lag, anti-lag, or space lag for a limit cycle. In such situations, the diffusion is due to particles pedalling and eddy/swirling motion on top of translatory motion via transient chaos. Also, the trajectories of the two particles in the state space resemble a Chiral Phenomenon.

nlin.CD↗

arXiv2022

Dynamics of a Charged Thomas Oscillator in an External Magnetic Field

In this letter, we provide a detailed numerical examination of the dynamics of a charged Thomas oscillator in an external magnetic field. We do so by adopting and then modifying the cyclically symmetric Thomas oscillator to study the dynamics of a charged particle in an external magnetic field. These dynamical behaviours for weak and strong field strength parameters fall under two categories; conservative and dissipative. The system shows a complex quasi-periodic attractor whose topology depends on initial conditions for high field strengths in the conservative regime. There is a transition from adiabatic motion to chaos on decreasing the field strength parameter. In the dissipative regime, the system is chaotic for weak field strength and weak damping but shows a limit cycle for high field strengths. Such behaviour is due to an additional negative feedback loop that comes into action at high field strengths and forces the system dynamics to be stable in periodic oscillations. For weak damping and weak field strength, the system dynamics mimic Brownian motion via chaotic walks.

nlin.CD↗

arXiv2020

Pattern in non-linearly coupled network of identical Thomas oscillators

We have investigated synchronized pattern in a network of Thomas oscillators coupled with sinusoidal nonlinear coupling. Pattern like chimera states are not only observed for many non-locally coupled oscillators but there is a signature of it even for locally coupled few oscillators. For certain range of intermediate coupling, clusters are also observed. These patterns do resemble with motion of real self propelled coupled dynamical systems.

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