Qualitative Theory of Dynamical Systems

Article	Citations
Approximate Controllability of a Coupled Nonlocal Partial Functional Integro-differential Equations with Impulsive Effects	93
Some New Results on Itô–Doob Hadamard Fractional Stochastic Pantograph Equations in $$L^p$$ Spaces	84
Abelian Integrals and Non-generic Turning Points	84
Existence of Homoclinic Solutions for the Discrete p(k)-Laplacian Operator	69
Dynamics of One-Dimensional Motion of a Gas Under the Influence of Monochromatic Radiation	57
Exact Solutions and Dynamical Behaviors of the Raman Soliton Model with Anti-Cubic Nonlinearity	44
Nonlinear Multi-term Impulsive Fractional q-Difference Equations with Closed Boundary Conditions	38
Cosmic-Plasma Environment, Singular Manifold and Symbolic Computation for a Variable-Coefficient (2+1)-Dimensional Zakharov-Kuznetsov-Burgers Equation	36
Ground State and Sign-Changing Solutions for Critical Schrödinger–Poisson System with Lower Order Perturbation	28
Globally Exponential Stability of Piecewise Pseudo Almost Periodic Solutions for Neutral Differential Equations with Impulses and Delays	26
Bifurcation of Limit Cycles and Isochronous Centers on Center Manifolds for a Class of Cubic Kolmogorov Systems in $${\mathbb {R}}^{3}$$	26
Existence of Traveling Wave Solutions for Gardner Equation and Its Spatiotemporal Delay Form	25
q-Pressure for Dynamical Systems	24
A Note on Asymptotic Stability of Semilinear Thermoelastic System	24
Modulation Analysis for Stochastic FitzHugh–Nagumo Type Equation with Time Delay	23
Coexistence of Analytic and Piecewise Analytic Limit Cycles in Planar Piecewise Quadratic Differential Systems	23
Dynamical Behavior and Exact Explicit Traveling Wave Solutions of a Generalized Vakhnenko-Parkes Equation	23
Lie Subalgebras, Solutions and Conserved Vectors of a Nonlinear Geophysical Korteweg de Vries Equation in Ocean Physics and Nonlinear Mechanics with Power Law	23
On the Sharp Existence of Normalized Ground State Solutions for Non-Autonomous Kirchhoff Equations	22
A Study on the Approximate Controllability of Damped Elastic Systems Using Sequence Method	21
On Separable Cubic Stochastic Operators	20
KAM Tori for a Two Dimensional Beam Equation with a Quintic Nonlinear Term and Quasi-periodic Forcing	20
A New Approach on the Approximate Controllability Results for Hilfer Fractional Stochastic Hemivariational Inequalities of Order $$1<\mu <2$$	20
The Existence of Evolution Systems of Measures of Non-autonomous Stochastic Differential Equations with Infinite Delays	19
Response Solutions of Degenerate Quasi-Periodic Systems Under Small Perturbations	19

Boundedness and Partial Convergence of Solution of a Class of Stochastic Differential Equations	19
Codimension-Two Bifurcation in a Class of a Discrete-Time Predator–Prey Interaction with Cannibalism	19
Hyers-Ulam Stability to Linear Nonhomogeneous Quaternion-Valued Matrix Difference Equations via Complex Representation	18
Stability Analysis of Second Order Impulsive Differential Equations	18
Lie Symmetries and Exact Solutions of KdV–Burgers Equation with Dissipation in Dusty Plasma	18
Topological Entropy of a Factor Map Under Amenable Group Actions	17
Existence of Periodic Solutions for a Class of Dynamic Equations with Multiple Time Varying Delays on Time Scales	17
Complex Dynamics for an Immunosuppressive Infection Model with Virus Stimulation Delay and Nonlinear Immune Expansion	17
New Results for Some Damped Dirichlet Problems with Impulses	17
Solvability and Hyers-Ulam Stability of Quaternion Difference Equations With Two-sided Coefficients	17
pth Moment Exponential Stability of Impulsive Stochastic Functional Differential Equations	16
Degenerate Transcritical Bifurcation Point can be an Attractor: A Case Study in a Slow–Fast Modified Leslie–Gower Model	16
New Variational Principles of Topological Pressures	16
Limit Cycles in Discontinuous Planar Piecewise Differential Systems with Multiple Nonlinear Switching Curves	16
Generalized Trial Equation Scheme and Enhance Modified Extended Tanh Function Method with Nonparaxial Pulse Propagation to the Cubic–Quintic Nonlinear Helmholtz Equation	15
Relative Controllability and Hyers–Ulam Stability of Riemann–Liouville Fractional Delay Differential System	15
Continuous Dependence and Differentiability of Solutions of Second-Order Impulsive Differential Equations on Initial Values and Impulsive Points	15
Hopf Bifurcation Analysis of a Predator–Prey Model with Prey Refuge and Fear Effect Under Non-diffusion and Diffusion	15
Hyperbolicity, Shadowing, and Bounded Orbits	15
Lyapunov Functions for Investigating Stability Properties of a Fractional-Order Computer Virus Propagation Model	15
Switched Server Systems Whose Parameters are Normal Numbers in Base 4	15
Symbolically Computing the Shallow Water via a (2+1)-Dimensional Generalized Modified Dispersive Water-Wave System: Similarity Reductions, Scaling and Hetero-Bäcklund Transformations	14
Qualitative Investigation of Nonlinear Fractional Coupled Pantograph Impulsive Differential Equations	14
Disease Dynamics of a Probabilistic Model with Vaccination Under Regime Switching	14
Normalized Solutions for Schrödinger Equations with Local Superlinear Nonlinearities	14
Periodic Wave Solution of the Generalized Burgers–Fisher Equation via Abelian Integral	14
Pontryagin Maximum Principle for Fractional Delay Differential Equations and Controlled Weakly Singular Volterra Delay Integral Equations	14
Some Notes on Topological Entropy of Subsets on Compact Uniform Spaces	13
On Unbounded Motions in a Real Analytic Bouncing ball Problem	13
Rich Dynamics of Discrete Time-Delayed Moran-Ricker Model	13
On a Certain Class of IFSs and Their Attractors	13
Coexistence of Limit Cycles and Homoclinic Loops in a Leslie-Gower Model with Allee Effect	13
An Optimal Control Strategy for Antiretroviral Treatment of HIV Infection in Presence of Immunotherapy	13
Product Type Potential on the One-Dimensional Lattice Systems: Selection of Maximizing Probability and a Large Deviation Principle	13
Necessary Optimality Conditions for Singular Controls of Caputo Fractional Systems with Delay in Control	13
Expansive Measures of Nonautonomous Iterated Function Systems	13
Stochastic Dynamics of a Two-Species Patch-System With Ratio-Dependent Functional Response	13
Dynamics of N-Species Cooperation Models with Feedback Controls and Continuous Delays	13
Geometric Scattering Monodromy	13
Existence of Ground State Solutions for Generalized Quasilinear Schrödinger Equations with Asymptotically Periodic Potential	12
Dynamics of a Stochastic Brucellosis Model with Vaccination and Environmental Pollution Transmission	12
Local Integrability and Linearizability for Three Dimensional Lotka–Volterra Cubic Systems	12
Existence of Solutions for p(x)-Laplacian Elliptic BVPs on a Variable Sobolev Space Via Fixed Point Theorems	12
Expressions and Evolution of Traveling wave Solutions in a Generalized Two-Component Rotation b-Family System	12
Estimates for the Number of Limit Cycles in Discontinuous Generalized Liénard Equations	12
Strong Pairs of Periodic Segments	11
Existence and Hyers–Ulam Stability of Jerk-Type Caputo and Hadamard Mixed Fractional Differential Equations	11
Heat Kernel Method for Quintic and Sextic Equations in Distributions and Hyperfunctions	11
Existence Results and Ulam–Hyers Stability for a Fully Coupled System of Nonlinear Sequential Hilfer Fractional Differential Equations and Integro-Multistrip-Multipoint Boundary Conditions	11
Spatiotemporal Dynamics in a Diffusive Predator–Prey System with Beddington–DeAngelis Functional Response	11

Sliding Cycles of Regularized Piecewise Linear Visible–Invisible Twofolds	10
Hyers–Ulam Stability for a Coupled System of Fractional Differential Equation With p-Laplacian Operator Having Integral Boundary Conditions	10
Sufficient Conditions to have Global Centers via Branching Theory	10
Four Limit Cycles of Discontinuous Piecewise Differential Systems with Nilpotent Saddles Separated by a Straight Line	10
Infinitesimal Prolongation for Fractional Derivative $$\varPsi $$-Caputo Variable Order and Applications	10
Response Solutions for Nonlinear Oscillator Equation in High Order Degeneracy	10
Dynamics of Kirchhoff Wave Equations Incorporating Energy Damping Effects	10
Canonical Sequences of Optimal Quantization for Condensation Measures	10
Existence Results for the Solution of Abstract Neutral Impulsive Differential Problems with State-Dependent Delay	10
Bifurcation and Stability Analysis of a Discrete Predator–Prey Model with Alternative Prey	10
Quasi-periodic Solutions for a Generalized Higher-Order Boussinesq Equation	10
Minkowski Dimension and Slow–Fast Polynomial Liénard Equations Near Infinity	9
Approximate Controllability for Sobolev-Type Fuzzy Hilfer Fractional Neutral Integro-Differential Inclusion with Clarke Subdifferential Type	9
Relaxation Oscillation and Canard Explosion for a SIRS Model with Nonlinear Incidence Rate	9
Turing Patterns Induced by Cross-Diffusion in a Predator–Prey System with Functional Response of Holling-II Type	9
Dynamical Analysis of a Discrete Amensalism System with the Beddington–DeAngelis Functional Response and Allee Effect for the Unaffected Species	9
Strong Resonance Bifurcations and State Feedback Control in a Discrete Prey-Predator Model with Harvesting Effect	9
On the Solutions of Ordinary Differential Equations in the Form of Dulac Series	9
Equivariant Nonautonomous Normal Forms	9
Novel Insight into a Single-Species Metapopulation Model with Time Delays	9
Natural Convection Non-Newtonian EMHD Dissipative Flow Through a Microchannel Containing a Non-Darcy Porous Medium: Homotopy Perturbation Method Study	9
Multiple Families of Bounded Solutions Near Perturbed Homoclinic Orbits, Application to a Nonlinear Wave Equation	9
Boundedness of Traveling Waves in a Discrete Diffusion Model with Delay	9
Some Existence Results of Coupled Hilfer Fractional Differential System and Differential Inclusion on the Circular Graph	8
A Study on Fractional Differential Equations with a Generalized Exponential Kernel Derivative	8
Several Continuities of a Pullback Random Attractor for Stochastic Non-Autonomous Zakharov Lattice Equations	8
Existence and Approximate Controllability Results for the Second-Order Abstract Neutral Differential System with Damping	8
A Note on the Stationary Probability Density Function and Covariance Matrix of a Stochastic Chemostat Model with Distributed Delay	8
Trajectory Controllability of Impulsive Neutral Stochastic Functional Integrodifferential Equations Driven by fBm with Noncompact Semigroup via Mönch Fixed Point	8
An Investigation on the Approximate Controllability of Non-instantaneous Impulsive Hilfer Sobolev-Type Fractional Stochastic System Driven by the Rosenblatt Process and Poisson Jumps	8
Homological Data on the Periodic Structure of Self-Maps on Wedge Sums	8
Global Hopf Bifurcation of a Diffusive Modified Leslie–Gower Predator–Prey Model with Delay and Michaelis–Menten Type Prey Harvesting	8
On a Rumor Propagation Model with Spatial Heterogeneity	8
Orbit Growth of Sofic Shifts and Periodic-Finite-Type Shifts	8
On the Number of Positive Solutions for a Higher Order Elliptic System	7
Rotation Domains and Stable Baker Omitted Value	7
Infinitely Many Nodal Solutions for Kirchhoff-Type Equations with Non-odd Nonlinearity	7
Multiplicity of Solutions for Non-homogeneous Dirichlet Problem with One-Dimension Minkowski-Curvature Operator	7
Blow-Up Behaviors of Minimizers for the $$\dot{H}^{\gamma _c}$$-Critical Fourth-Order Nonlinear Schrödinger Equation with the Mixed Dispersions	7
Bifurcations, Permanence and Local Behavior of the Plant-Herbivore Model with Logistic Growth of Plant Biomass	7
Existence of Positive Solutions for (N, p)-Laplace Equation with Exponential Nonlinearity Term and Convection Term in Dimension $${\mathbb {N}}$$	7
Multiple Positive Periodic Solutions to Minkowski-Curvature Equations with a Singularity of Attractive Type	7
Elementary Integrability of Polynomial Rayleigh–Duffing Systems	7
Existence Results for Nonlinear Hilfer Pantograph Fractional Integrodifferential Equations	7
Bifurcations and Exact Peakons, Periodic Peakons, Solitary Wave, Kink Wave Solutions for the Quartic CH-Type Equation	7
Exponential Stabilization of a Flexible Structure: A Delayed Boundary Force Control Versus a Delayed Boundary Moment Control	7
Traveling Wave Solution with the Critical Speed for a Diffusive Epidemic System with Spatio-Temporal Delay	7
Higher-Order Nonlinear Dynamical Systems and Invariant Lagrangians on a Lie Group: The Case of Nonlocal Hunter–Saxton Type Peakons	7
Baby Mandelbrot Sets and Spines in Some One-Dimensional Subspaces of the Parameter Space for Generalized McMullen Maps	7
Global Phase Portrait and Local Integrability of Holomorphic Systems	7
On Multi Order Nonlinear Langevin Type of $$\mathbb {FDE}$$ Subject to Multi-Point Boundary Conditions	6
Innovative Insights into Wave Phenomena: Computational Exploration of Nonlinear Complex Fractional Generalized-Zakharov System	6
Strong Chain Transitivity via Uniformity	6
N-Soliton and Other Analytic Solutions for a ($$3 + 1$$)-Dimensional Korteweg–de Vries–Calogero–Bogoyavlenskii–Schiff Equation with the Time-Dependent Coefficients for the Shallow Water Waves	6
Bifurcations of a Generalized Heteroclinic Loop in a Planar Piecewise Smooth System with Periodic Perturbations	6
Asymptotic Behavior of Solutions to Difference Equations of Neutral Type	6
Interactions among the Rogue Waves and Solitons for a (2+1)-dimensional Maccari System in Fluid Mechanics and Nonlinear Optics	6
Bifurcation of Piecewise Smooth Manifolds from 3D Center-Type Vector Fields	6
N-Convergence and Chaotic Properties of Non-autonomous Discrete Systems	6
A Note on the Existence and Controllability Results for Fractional Integrodifferential Inclusions of Order $$r \in (1,2]$$ with Impulses	6
Specification and Shadowing Properties of Free Semigroup Actions	6
Two Weighted Norm Dynamic Inequalities with Applications on Second Order Half-Linear Dynamic Equations	6
On the Decay of Solutions of the Linearized Equations of Conservation Equations with Viscosity and Relaxation	6
Global Asymptotic Stability in Cubic Systems with a Nilpotent Point at the Origin and with An Invariant Straight Line	6
Existence of Periodic Solutions in the Systems of the Billiard Type	6
Morse Predecomposition of an Invariant Set	6
Bifurcations and Exact Traveling Wave Solutions for the Generalized Alexeyev’s $$A\pm $$ Equation	6
Well-Posedness of a Class of Fractional Langevin Equations	6
Fractional Evolution Equations with Nonlocal Initial Conditions and Superlinear Growth Nonlinear Terms	6
Quasi-Stationary Distribution of a Prey–Predator Model Driven by Demographic Stochasticity	6
Non–Equivalence Between the Melnikov and the Averaging Methods for Nonsmooth Differential Systems	6
A Polynomial System of Degree Four with an Invariant Square Containing At Least Five Limit Cycles	6
On Double Homoclinic Bifurcation of Limit Cycles in Near-Hamiltonian Systems on the Cylinder	6
Historic Behavior in Rock–Paper–Scissor Dynamics	6
Existence of Gibbs States and Maximizing Measures on a General One-Dimensional Lattice System with Markovian Structure	6
An Impulsive Predator–Prey System with Modified Leslie–Gower Functional Response and Diffusion	6
Riemann–Hilbert Approach and Multiple Arbitrary-Order Pole Solutions for the Lakshmanan–Porsezian–Daniel Equation with Finite Density Initial Data	6
Random Uniform Attractors for First Order Stochastic Non-Autonomous Lattice Systems	6
Quasilinear Coupled System in the Frame of Nonsingular ABC-Derivatives with p-Laplacian Operator at Resonance	6
Auto-Bäcklund Transformation and Exact Solutions for a New Integrable (3+1)-dimensional KdV-CBS Equation	6

On the Variational Principle for BS Dimension in Amenable Group Actions	6
Representation and Stability of Solutions for Impulsive Discrete Delay Systems with Linear Parts Defined by Non-Permutable Matrices	6
Filling Times for Linear Flow on the Torus with Truncated Diophantine Conditions: A Brief Review and New Proof	5
Bilinear Bäcklund Transformations, as well as N-Soliton, Breather, Fission/Fusion and Hybrid Solutions for a (3+1)-Dimensional Integrable Wave Equation in a Fluid	5
A van der Pol-Duffing Oscillator with Indefinite Degree	5
Integrable (3 + 1)-Dimensional Generalization for the Dispersionless Davey–Stewartson System	5
Transmission Dynamics of a High Dimensional Rabies Epidemic Model in a Markovian Random Environment	5
Oscillatory Behavior of Semi-canonical Nonlinear Neutral Differential Equations of Third-Order Via Comparison Principles	5
Existence and Regularity of Solutions to Damping Elastic System with State-Dependent Nonlocal Condition	5
The Controllability for Second-Order Semilinear Impulsive Systems	5
Second-Order Noncanonical Delay Differential Equations with Sublinear and Superlinear Terms: New Oscillation Criteria via Canonical Transform and Arithmetic–Geometric Inequality	5
Qualitative Analysis for an HIV Infection Model with Caspase-1-Mediated Pyroptosis of the Predominance: Threshold Dynamics and Traveling Waves	5
Exploring Discrete-Time Epidemic Behavior Based on Saturated Incidence Rate and Multiple Transmission Pathways	5
Sufficient Conditions and Bounds Estimate of Blow-Up Time for a Fourth Order Parabolic Equation	5
Nonlinear Dynamical Analysis and Optimal Control Strategies for a New Rumor Spreading Model with Comprehensive Interventions	5
Representation of a Solution for a Neutral Type Differential Equation with Pure Delay on Fractal Sets	5
Approximate Controllability for Semilinear Fractional Stochastic Evolution Equations	5
Exactly Solvable Quadratic Differential Equation Systems Through Generalized Inversion	5
Isochronicity Conditions and Lagrangian Formulations of the Hirota Type Oscillator Equations	5
Structurally Unstable Quadratic Vector Fields of Codimension Two: Families Possessing One Finite Saddle-Node and a Separatrix Connection	5
Generalized Fractional Differential Systems with Stieltjes Boundary Conditions	5
On the Bielecki–Hyers–Ulam Stability of Non–linear Impulsive Fractional Hammerstein and Mixed Integro–dynamic Systems on Time Scales	5
Persistence of Invariant Tori in Infinite-Dimensional Hamiltonian Systems	5
Phase Portraits of the Family IV of the Quadratic Polynomial Differential Systems	5
Dynamic Analysis of a Toxin-Producing Phytoplankton Zooplankton Model with Allee Effect	5
Hilbert Number for a Family of Piecewise Nonautonomous Equations	5
Stochastic Averaging of Non-linear Implicit Caputo’s Fractional Differential Equation with Multiplicative Fractional Brownian Motion	5
On Generalized Two Dimensional Linear Hybrid Dynamical Systems	4
Dimension of a Class of Intrinsically Transversal Solenoidal Attractors in High Dimensions	4
Bifurcation Analysis and Soliton Solutions to the Kuralay Equation Via Dynamic System Analysis Method and Complete Discrimination System Method	4
Breather Transitions and Their Mechanisms of a (2+1)-Dimensional Sine-Gordon Equation and a Modified Boussinesq Equation in Nonlinear Dynamics	4
Bielecki–Ulam’s Types Stability Analysis of Hammerstein and Mixed Integro–Dynamic Systems of Non–Linear Form with Instantaneous Impulses on Time Scales	4
Periodic Solutions of a Second Order Discontinuous Nonautonomous Differential Equation	4
Titchmarsh–Weyl Theory for Impulsive Dynamic Dirac System	4
Dynamics of Travelling Waves to KdV–Burgers–Kuramoto Equation with Marangoni Effect Perturbation	4
Qualitative Results of Non-linear Adjoint Dynamic System with Delays and Impulses on Arbitrary Time Domains	4
Global Dynamics of 3D Type-K Competitive Lotka-Volterra System with the Identical Intrinsic Growth Rate	4
General Solutions of a Class of nth-Order Nonlocal Differential Equations	4
Dynamical Study of Newly Created Analytical Solutions, Bifurcation Analysis, and Chaotic Nature of the Complex Kraenkel–Manna–Merle System	4
On the Stability of Hybrid Polycycles	4
Solitons, Breathers and Modulation Instability for a Higher-Order Coupled Nonlinear Schrödinger System for the Ultrashort Optical Pulses in a Nonlinear Medium	4
Ground State Sign-Changing Solutions for a Schrödinger–Poisson System with Steep Potential Well and Critical Growth	4
A Class of New Solvable Nonlinear Isochronous Systems and Their Classical Dynamics	4
Traveling Wave Solution of Bad and Good Modified Boussinesq Equations with Conformable Fractional-Order Derivative	4
New Solitary Wave Solutions and Dynamical Behaviors of the Nonlinear Fractional Zakharov System	4
Oscillation and Nonoscillation for Nonlinear Delay Difference Equations by Phase Plane Analysis	4
Normalized Solutions to Biharmonic Equation with Bounded Potential and Mixed Power Nonlinearities	4
Analysis on the Controllability of Hilfer Fractional Neutral Differential Equations with Almost Sectorial Operators and Infinite Delay via Measure of Noncompactness	4
General Solution to a Nonlocal Linear Differential Equation of First-Order	4
Parameter Identification Problem for Semilinear Abstract Degenerate Delay Differential Equation	4
Dynamics of Predator–Prey Model Based on Fear Effect with Bifurcation Analysis and Chaos Control	4
Dirichlet Problems for Fractional Laplace Equations with Singular Nonlinearity	4
A Qualitative Study for Two Discrete Fractional Delta Difference BVPs with Falling Functions: Application on the Temperature Control System	4
A Variational Principle of the Deformed Entropy	4
Ground State Solutions for Generalized Quasilinear Schrödinger Equations with Critical Growth	4
An Improved Reciprocally Convex Inequality and its Application to Time-Varying Delay Systems	4
Streams and Graphs of Dynamical Systems	4
Hausdorff Dimension of the Exceptional Set of Interval Piecewise Affine Contractions	4
On the Menger Probabilistic Bipolar Metric Spaces: Fixed Point Theorems and Applications	4
On $$(\alpha ,\nu )$$-Relaxed Polygonal Metric Spaces and Fixed Point Results	4
An Age-Structured Diffusive Model for Epidemic Modelling: Lie Symmetries and Exact Solutions	4
Bifurcation of Limit Cycles of a Piecewise Smooth Hamiltonian System	4
Nonlinear Second Order Delay Dynamic Equations on Time Scales: New Oscillatory Criteria	4
Total Collision in a Four-Body Problem with Jacobi Potential	4
Qualitative Analysis, Chaotic Behavior and Optical Solitons Perturbation for the Coupled Fokas-Lenells System in Birefringent Fibers	4
Global Stability and Permanence of a Discrete-Time Two-Predators One-Prey System with Holling Type-III Response	4
Riemann–Hilbert Approach and N-Soliton Solutions of a Novel n-Component Shifted Nonlocal Reverse-Time NLS Equation	4
Exploring the Impact of Distributed Delay and Environmental Fluctuation on Food Chain Stability in a Chemostat Model	4
Asymptotic and Oscillatory Behaviour of Third Order Non-linear Differential Equations with Canonical Operator and Mixed Neutral Terms	4
Lie–Backlund Symmetry Generators and a Variety of Novel Periodic-Soliton Solutions to the Complex-Mode of Modified Korteweg-de Vries Equation	4
Analysis of Neutral Fractional Differential Equation via the Method of Upper and Lower Solution	4
Normalized Solutions for the Fractional Choquard Equations with Hardy–Littlewood–Sobolev Upper Critical Exponent	4