arXiv subjects

V. R. Saiprasad

Publications and source records attributed to V. R. Saiprasad.

4 recordsLinked to original sources

arXiv2026

A New Route to Chaos through the Geometric Composition of Non-Normal Amplification

Chaos emerges when stretching is repeatedly recycled by reinjection. We uncover a new route to chaos in which the decisive variable is the temporal order of non-normal tangent maps: periodic and chaotic states can share essentially the same one-step stretching statistics while their ordered products acquire opposite Lyapunov growth. We introduce the ordered-product growth rate $h_L$ over $L$ successive tangent maps, which reveals how states indistinguishable at one step separate under geometric composition and identifies the finite composition scale at which chaos emerges. We use this mechanism to establish a new form of global chaos control: minute phase actions reorient the successive non-normal amplification directions so that their geometric composition becomes contracting, suppressing chaos at fixed dissipation without reducing local amplification or targeting a preselected orbit.

nlin.CD↗

arXiv2026

Inferring Non-Normal Amplification Geometry from Multivariate Time Series

Across hydrodynamics, ecology, neuroscience, network dynamics, non-Hermitian physics, and socio-economic systems, asymptotically stable dynamics can exhibit large transient amplifications that are invisible to eigenvalue-based analyses. The mechanism is geometric rather than spectral: perturbations entering along one direction may be expressed transiently along another, allowing asymptotic decay to coexist with strong transient or noise-driven amplification. We introduce non-normal directional response inference, a data-driven method for detecting this geometry from multivariate time series when the governing operator is unknown. A local linear operator is estimated from sliding windows and projected onto the dominant two-dimensional input-response subspace. The reduced dynamics are summarized by the eigenvalue splitting $Δ$, eigenvector non-orthogonality $K$, and the scale-free ratio $R=K/K_c(Δ)$, where $K_c(Δ)$ is the two-dimensional threshold for transient amplification. Controlled benchmarks show that the reduced geometry, particularly $R$, can be recovered from finite data even when the full high-dimensional operator is poorly estimated. Tests across sample size, dimension, training horizon, spectral structure, and non-stationarity confirm that the relevant response geometry requires far fewer observations than full-matrix recovery. Applied in moving windows to electrohysterogram, seizure EEG, freezing-of-gait, and unstable push-up inertial recordings, the method reveals systematic changes around known physiological or behavioral episodes through shifts in $R$, changes in $Δ$, or stronger projection of fluctuations onto the inferred response direction. It thus exposes interpretable changes in local response geometry without framing the problem as supervised event detection.

physics.data-an↗

arXiv2026

Non-Normal Route to Chaos

Deterministic chaos is usually associated with local spectral expansion: Jacobian eigenvalues are expected to exceed unity somewhere on the attractor. We show that this view is incomplete in dimensions d>1. For non-normal Jacobians, pointwise spectral stability can suggest everywhere local contraction, while non-orthogonal eigenvectors still allow transient singular-vector amplification. We construct four low-dimensional deterministic maps realizing this mechanism: partition-reinjected, phase-prescribed, feedback-driven, and affine-reinjected non-normal routes to chaos. In all cases, the instantaneous Jacobian remains spectrally stable on the attractor, with eigenvalues fixed inside the unit disk, while increasing non-normality drives the maximal Lyapunov exponent through zero. The positive exponent therefore describes sustained asymptotic chaos, not transient chaos. Across the four classes, the common signature is spectral radius $ρ_{\mathrm{traj}}^{\max}<1$, singular value $σ_{\mathrm{traj}}^{\max}>1$ maximum Lyapunov exponent $λ_1>0$, and an increase of attractor dimension. These examples identify non-normality and recurrent reinjection of transiently amplified directions as a deterministic route to chaos distinct from eigenvalue instability.

nlin.CD↗

arXiv2022

Analysis of COVID-19 in India using vaccine epidemic model incorporating vaccine effectiveness and herd immunity

COVID-19 will be a continuous threat to human population despite having a few vaccines at hand until we reach the endemic state through natural herd immunity and total immunization through universal vaccination. However, the vaccine acts as a practical tool for reducing the massive public health problem and the emerging economic consequences that the continuing COVID -19 epidemic is causing worldwide, while the vaccine efficacy wanes. In this work, we propose and analyze an epidemic model of Susceptible-Exposed-Infected-Recovered-Vaccinated (SEIRV) population taking into account the rate of vaccination and vaccine waning. The dynamics of the model has been investigated, and the condition for a disease-free endemic equilibrium state is obtained. Further, the analysis is extended to study the COVID-19 spread in India by considering the availability of vaccines and the related critical parameters such as vaccination rate, vaccine efficacy and waning of vaccine's impact on deciding the emerging fate of this epidemic. We have also discussed the conditions for herd immunity due to vaccinated individuals among the people. Our results highlight the importance of vaccines, the effectiveness of booster vaccination in protecting people from infection, and their importance in epidemic and pandemic modelling.

q-bio.PE↗