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Items from 1 to 20 out of 733 results

article

Stability analysis of a class of switched linear systems on non-uniform time domains

Fatima Zohra Taousser, Michael Defoort, Mohamed Djemai, F.Z. Taousser, more

Systems & Control Letters > 2014 > 74 > Complete > 24-31

This paper deals with the stability analysis of a class of switched linear systems on non-uniform time domains. The considered class consists of a set of linear continuous-time and linear discrete-time subsystems. First, some conditions are derived to guarantee the exponential stability of this class of systems on time scales with bounded graininess function when the subsystems are exponentially stable...

article

Reduction of discrete‐time infectious disease models

Rafael Bravo de la Parra

Mathematical Methods in the Applied Sciences > 46 > 12 > 12454 - 12472

In this work, we propose the construction of discrete‐time systems with two time scales in which infectious diseases dynamics are involved. We deal with two general situations. In the first, we consider that individuals affected by the disease move between generalized sites on a faster time scale than the dynamics of the disease itself. The second situation includes the dynamics of the disease acting...

article

Synchronization of time scales switched complex networks via impulsive couplings

Yong Pei, Churong Chen, Dechang Pi

Mathematical Methods in the Applied Sciences > 46 > 9 > 10624 - 10641

We investigate the asymptotic synchronization problem of switched complex networks (SCNs) on time scales. Switches are made by a following time sequence with a dwell time constraint. By designing a Lyapunov function and a matrix inequality, self‐synchronizing criteria for SCNs are derived based on time scales theory. An impulsive coupling approach is designed to control links between nodes at the...

article

Controllability analysis of nonlinear switched singular system on time scales

Bhim Kumar, Muslim Malik

Asian Journal of Control > 25 > 3 > 2345 - 2359

In this manuscript, we establish the controllability results for a nonlinear singular switched system on arbitrary time scales. We used the mathematical induction to evaluate the solution of the nonlinear slow switched subsystem and nonlinear fast switched subsystem. Also, we study the necessary and sufficient conditions for the controllability of the nonlinear singular switched system followed by...

article

Characteristic time scales of evaporation from a subarctic reservoir

Adrien Pierre, Daniel F. Nadeau, Antoine Thiboult, Alain N. Rousseau, more

Hydrological Processes > 37 > 3 > n/a - n/a

Water bodies such as lakes and reservoirs affect the regional climate by acting as heat sinks and sources through the evaporation of substantial quantities of water over several months of the year. Unfortunately, energy exchange observations between deep reservoirs and the atmosphere remain rare in northeastern North America, which has one of the highest densities of water bodies in the world. This...

article

The heat equation on time scales

Tom Cuchta, Rui A. C. Ferreira

Opuscula Mathematica > 2023 > Vol. 43, no. 4 > 475--491

We present the use of a Fourier transform on time scales to solve a dynamic heat IVP. This is done by inverting a certain exponential function via contour integral. We include some specific examples and directions for further study.

article

Controllability of singular dynamic systems on time scales

Muslim Malik, Mohammad Sajid, Vipin Kumar

Asian Journal of Control > 24 > 5 > 2771 - 2777

In this work, we investigate the controllability of singular dynamic systems on time scales. First, we decompose the consider systems into a slow subsystem and a fast subsystem. After that, we use the Laplace transform and convolution theorem to derive the state response of these two subsystems. Finally, we established some necessary and sufficient conditions for the controllability of the slow subsystem...

article

Time scale reachability and controllability of time‐varying linear systems

Bacem Ben Nasser, Mohamed Djemai, Michael Defoort, Taous‐Meriem Laleg‐Kirati

Asian Journal of Control > 24 > 5 > 2074 - 2088

In this paper, we investigate the analysis of reachability and controllability for time‐varying linear systems evolving on nonuniform time domains also known as arbitrary time scales. Based on appropriate operators, some necessary and sufficient conditions are derived to guarantee the reachability for this class of systems using linear algebra tools. Furthermore, a link between optimality and the...

article

Delay dynamic equations on isolated time scales and the relevance of one‐periodic coefficients

Martin Bohner, Tom Cuchta, Sabrina Streipert

Mathematical Methods in the Applied Sciences > 45 > 10 > 5821 - 5838

We are motivated by the idea that certain properties of delay differential and difference equations with constant coefficients arise as a consequence of their one‐periodic nature. We apply the recently introduced definition of periodicity for arbitrary isolated time scales to linear delay dynamic equations and a class of nonlinear delay dynamic equations. Utilizing a derived identity of higher order...

article

Periodicity on isolated time scales

Martin Bohner, Jaqueline Mesquita, Sabrina Streipert

Mathematische Nachrichten > 295 > 2 > 259 - 280

In this work, we formulate the definition of periodicity for functions defined on isolated time scales. The introduced definition is consistent with the known formulations in the discrete and quantum calculus settings. Using the definition of periodicity, we discuss the existence and uniqueness of periodic solutions to a family of linear dynamic equations on isolated time scales. Examples in quantum...

article

Total controllability results for a class of time‐varying switched dynamical systems with impulses on time scales

Vipin Kumar, Mohamed Djemai, Michael Defoort, Muslim Malik

Asian Journal of Control > 24 > 1 > 474 - 482

In this paper, we establish some necessary and sufficient conditions of the controllability results for a class of impulsive switched systems with non‐instantaneous jumps on time scales. Firstly, we define the solution of the considered problem by using the parameter variation method. We also define some Gramian matrices to establish the controllability results. Moreover, we give some conditions under...

article

On oscillatory behaviour of third-order half-linear dynamic equations on time scales

Said R. Grace, Gokula Nanda Chhatria

Opuscula Mathematica > 2022 > Vol. 42, no. 6 > 849--865

In this work, we study the oscillation and asymptotic behaviour of third-order nonlinear dynamic equations on time scales. The findings are obtained using an integral criterion as well as a comparison theorem with the oscillatory properties of a first-order dynamic equation. As a consequence, we give conditions which guarantee that all solutions to the aforementioned problem are only oscillatory,...

article

The dynamic analysis on a class of stochastic impulsive equations with doubly weighted pseudo almost automorphic coefficients on time scales

Ping Zhu

Mathematical Methods in the Applied Sciences > 44 > 17 > 13774 - 13790

This paper is devoted to exploring the translation invariance and convolution invariance of doubly weighted pseudo almost automorphic stochastic processes with impulses on time scales. Based on these results, the existence and uniqueness of the doubly weighted pseudo almost automorphic solutions to a class of stochastic nonlinear impulsive equations on time scales are obtained by taking advantage...

article

Asian meteorological droughts on three time scales and different roles of sea surface temperature and soil moisture

Yanting Zhang, Renguang Wu

International Journal of Climatology > 41 > 13 > 6047 - 6064

The present study utilizes the standard precipitation index (SPI) to differentiate Asian summer droughts that are associated with variations of precipitation over periods of 3, 9 and 24 months (termed as short‐term, medium‐term and long‐term droughts, respectively). Then, the relationships between these droughts and atmospheric circulation, sea surface temperature (SST), and soil moisture are investigated...

article

Permanence, existence, and stability of almost automorphic solution of a non‐autonomous Leslie–Gower prey–predator model with control feedback terms on time scales

Soniya Dhama, Syed Abbas

Mathematical Methods in the Applied Sciences > 44 > 15 > 11783 - 11796

A general non‐autonomous Leslie–Gower prey–predator model on time scales with control input terms is examined in the present paper. The significant property permanence is established along with the existence of almost automorphic solution of the model system. By constructing a suitable Lyapunov functional, presence of a one of a kind all‐around attractive positive almost automorphic solution of the...

article

Identifying dominant environmental predictors of freshwater wetland methane fluxes across diurnal to seasonal time scales

Sara H. Knox, Sheel Bansal, Gavin McNicol, Karina Schafer, more

Global Change Biology > 27 > 15 > 3582 - 3604

While wetlands are the largest natural source of methane (CH₄) to the atmosphere, they represent a large source of uncertainty in the global CH₄ budget due to the complex biogeochemical controls on CH₄ dynamics. Here we present, to our knowledge, the first multi‐site synthesis of how predictors of CH₄ fluxes (FCH4) in freshwater wetlands vary across wetland types at diel, multiday (synoptic), and...

article

Commutativity of quaternion‐matrix–valued functions and quaternion matrix dynamic equations on time scales

Zhien Li, Chao Wang, Ravi P. Agarwal, Donal O'Regan

Studies in Applied Mathematics > 146 > 1 > 139 - 210

In this paper, we obtain some basic results of quaternion algorithms and quaternion calculus on time scales. Based on this, a Liouville formula and some related properties are derived for quaternion dynamic equations on time scales through conjugate transposed matrix algorithms. Moreover, we introduce the quaternion matrix exponential function by homogeneous quaternion matrix dynamic equations. Also...

article

Modeling the hazard of transition into the absorbing state in the illness‐death model

Elena Tassistro, Davide Paolo Bernasconi, Paola Rebora, Maria Grazia Valsecchi, more

Biometrical Journal > 62 > 3 > 836 - 851

The illness‐death model is the simplest multistate model where the transition from the initial state 0 to the absorbing state 2 may involve an intermediate state 1 (e.g., disease relapse). The impact of the transition into state 1 on the subsequent transition hazard to state 2 enables insight to be gained into the disease evolution. The standard approach of analysis is modeling the transition hazards...

article

Oscillation of first‐order dynamic equations with nonmonotone delay

Özkan Öcalan

Mathematical Methods in the Applied Sciences > 43 > 7 > 3954 - 3964

Consider the first‐order dynamic equations where

p \in C_{r d} ({[t_{0}, \infty)}_{T}, R^{+}),

τ \in C_{r d} ({[t_{0}, \infty)}_{T}, T)

and

τ (t) \leq t, \lim_{t \to \infty} τ (t) = \infty

. Under the assumption that the

τ (t)

is not necessarily monotone, we present new sufficient conditions for the oscillation of first‐order delay dynamic equations on time scales.

article

Analogy of classical and dynamic inequalities merging on time scales

Muhammad Jibril Shahab Sahir

Journal of Mathematics and Applications > 2020 > Vol. 43 > 139--152

In this paper, we present analogues of Radon’s inequality and Nesbitt’s inequality on time scales. Furthermore, we find refinements of some classical inequalities such as Bergström’s inequality, the weighted power mean inequality, Cauchy–Schwarz’s inequality and Hölder’s inequality. Our investigations unify and extend some continuous inequalities and their corresponding discrete analogues.

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Search results

Stability analysis of a class of switched linear systems on non-uniform time domains

Reduction of discrete‐time infectious disease models

Synchronization of time scales switched complex networks via impulsive couplings

Controllability analysis of nonlinear switched singular system on time scales

Characteristic time scales of evaporation from a subarctic reservoir

The heat equation on time scales

Controllability of singular dynamic systems on time scales

Time scale reachability and controllability of time‐varying linear systems

Delay dynamic equations on isolated time scales and the relevance of one‐periodic coefficients

Periodicity on isolated time scales

Total controllability results for a class of time‐varying switched dynamical systems with impulses on time scales

On oscillatory behaviour of third-order half-linear dynamic equations on time scales

The dynamic analysis on a class of stochastic impulsive equations with doubly weighted pseudo almost automorphic coefficients on time scales

Asian meteorological droughts on three time scales and different roles of sea surface temperature and soil moisture

Permanence, existence, and stability of almost automorphic solution of a non‐autonomous Leslie–Gower prey–predator model with control feedback terms on time scales

Identifying dominant environmental predictors of freshwater wetland methane fluxes across diurnal to seasonal time scales

Commutativity of quaternion‐matrix–valued functions and quaternion matrix dynamic equations on time scales

Modeling the hazard of transition into the absorbing state in the illness‐death model

Oscillation of first‐order dynamic equations with nonmonotone delay

Analogy of classical and dynamic inequalities merging on time scales

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