{"title":"Dynamic Complexities in Competing Parasitoid Species on a Shared Host","authors":"Lijiao Jia, Yunil Roh, Guangri Piao, Il Hyo Jung","doi":"10.1142/s0218127424500147","DOIUrl":"https://doi.org/10.1142/s0218127424500147","url":null,"abstract":"<p>In this study, we extend the two-dimensional host–parasitoid model to a one-host–two-parasitoid model, whose dynamic behaviors are more complex. As evidence, exploring the dynamic interaction between a host and its parasitoids provides significant insight into the biological control. Specifically, we demonstrate the existence of equilibrium points and explore their local stability properties, which are concerned with the effective biological control project. Furthermore, the transition between population fluctuations and the steady state is achieved via a bifurcation process, and we derive the occurrence conditions of the Neimark–Sacker bifurcation in the proposed system using an explicit criterion. To control population fluctuations and chaotic behaviors, two feedback control strategies are implemented in this system. Finally, the numerical simulations support our theoretical results and show the related biological phenomena.</p>","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154428","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Optimal and Poor Synchronizations of Directionally Coupled Phase-Coherent Chaotic Oscillators","authors":"Yong Lei, Xin-Jian Xu, Xiaofan Wang","doi":"10.1142/s0218127424500238","DOIUrl":"https://doi.org/10.1142/s0218127424500238","url":null,"abstract":"<p>We study directionally coupled phase-coherent chaotic oscillators in complex networks. We introduce an adjusted Lyapunov function that incorporates the frequencies of the oscillators and the interaction structure. Using the well-known Rössler system as an example, we address two optimization problems: frequency allocation and network design. Through numerical experiments, we demonstrate that the systematic synchrony can be effectively enhanced or inhibited by minimizing or maximizing the objective function, respectively. We then delve into the relationship between the structural and dynamical properties that lead to optimal synchronization. Interestingly, we observe a positive correlation between nodal in-degrees and frequency magnitudes, indicating that nodes with higher in-degrees tend to exhibit larger frequency magnitudes. On the other hand, we also find a negative correlation between nodal frequency and adjacent in-frequencies, suggesting that nodes with higher frequencies tend to be surrounded by nodes with lower frequency values. Finally, we explore the connections between degree correlations and optimal synchronization. We find that when minimizing the objective function, the presence of degree correlations always inhibits the systematic synchrony for frequency allocation, while the act of network design causes the correlations to become negative.</p>","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154035","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Study of Short-Term and Long-Term Memories by Hodgkin–Huxley Memristor","authors":"L. Wen, C. K. Ong","doi":"10.1142/s0218127424500408","DOIUrl":"https://doi.org/10.1142/s0218127424500408","url":null,"abstract":"<p><i>Long-term memory</i> (<i>LTM </i>) and <i>short-term memory</i> (<i>STM </i>) and their evolution from one to the other are important mechanisms to understand brain memory. We use <i>the Hodgkin–Huxley (HH ) model</i>, a well-tested and closest model to biological neurons and <i>synapses</i>, to shine some light on <i>LTM</i> and <i>STM</i> memorization mechanisms. The role of <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mstyle><mtext mathvariant=\"normal\">Na</mtext></mstyle></mrow><mrow><mo stretchy=\"false\">+</mo></mrow></msup></math></span><span></span> and <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mstyle><mtext mathvariant=\"normal\">K</mtext></mstyle></mrow><mrow><mo stretchy=\"false\">+</mo></mrow></msup></math></span><span></span><i>ion channels</i> playing in <i>LTM</i> and <i>STM</i> process is carefully examined by using three different types of input signals, namely, a <i>step DC voltage</i>, a <i>positive part of sinusoidal wave</i> and <i>periodic square signal with read voltage</i>. Results are analyzed based on <i>first</i>-<i>order</i><span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mstyle><mtext mathvariant=\"normal\">K</mtext></mstyle></mrow><mrow><mo stretchy=\"false\">+</mo></mrow></msup></math></span><span></span><i>memristor</i> and <i>second</i>-<i>order</i><span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mstyle><mtext mathvariant=\"normal\">Na</mtext></mstyle></mrow><mrow><mo stretchy=\"false\">+</mo></mrow></msup></math></span><span></span><i>memristor</i>.</p>","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154119","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Stability, Bifurcation and Dynamics in a Network with Delays","authors":"Xu Xu, Jianming Liu","doi":"10.1142/s0218127424500251","DOIUrl":"https://doi.org/10.1142/s0218127424500251","url":null,"abstract":"<p>In real-world networks, due to complex topological structures and uncertainties such as time delays, uncontrolled systems may generate instability and complexity, thereby degrading network performance. This paper provides a detailed analysis of the stability, Hopf bifurcation, and complex dynamics of a networked system under delayed feedback control. Based on the linear stability method and Hopf bifurcation theorem, the stability of the equilibrium of the error system and the existence of Hopf bifurcation are studied. The stability of periodic solutions bifurcating from the trivial equilibrium is analyzed using normal form theory and central manifold theorem. Special focus is on the effects of the network topology and time delays on the stability and Hopf bifurcation. The theoretical results are also extended to the complex networks with asymmetric adjacent matrices. In addition, the controlled model exhibits complicated dynamical behavior via three types of codimension two bifurcations and period-doubling bifurcations that eventually lead to chaos. Numerical experiments have validated the theoretical results and indicated that delayed feedback control can effectively generate or annihilate the complicated behavior of complex networks.</p>","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154244","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Dynamic Relationship Between Informal Sector and Unemployment: A Mathematical Model","authors":"A. K. Misra, Mamta Kumari","doi":"10.1142/s0218127424500184","DOIUrl":"https://doi.org/10.1142/s0218127424500184","url":null,"abstract":"<p>Shortage of formal jobs, lack of skills in workforce and increasing human population proliferate the informal sector. This sector provides an opportunity to unskilled workers to gain skills along with earnings. In this paper, a deterministic nonlinear mathematical model is developed to study the effects of informal skill learning and job generation on unemployment. For the formulated system, feasibility of equilibria and their stability properties are discussed. A pertinent quantity (<span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi mathvariant=\"cal\">ℛ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span><span></span>), known as the reproduction number, is calculated and it is shown that the formulated system undergoes transcritical, saddle-node, Hopf and Bogdanov–Takens bifurcations on the variation of <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi mathvariant=\"cal\">ℛ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span><span></span>. The analytically obtained results are validated through numerical simulations. The results obtained from this study indicate that a substantial rate of job generation by self-employed individuals has a stabilizing effect on the system. Moreover, self-employment along with informal skill acquisition through engaging in informal work proves to be an effective measure in curbing the issue of unemployment in society.</p>","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154126","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Lili Huang, Shaotian Wang, Tengfei Lei, Keyu Huang, Chunbiao Li
{"title":"Coupled HR–HNN Neuron with a Locally Active Memristor","authors":"Lili Huang, Shaotian Wang, Tengfei Lei, Keyu Huang, Chunbiao Li","doi":"10.1142/s0218127424500226","DOIUrl":"https://doi.org/10.1142/s0218127424500226","url":null,"abstract":"<p>Local activity could be the source for complexity. In this study, a multistable locally active memristor is proposed, whose nonvolatile memory, as well as locally active characteristics, is validated by the power-off plot and DC <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>V</mi></math></span><span></span>–<span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>I</mi></math></span><span></span> plot. Based on the two-dimensional Hindmarsh–Rose neuron and a one-dimensional Hopfield neuron, a simple neural network is constructed by connecting the two neurons with the locally active memristor. Coexisting multiple firing patterns under different initial conditions are investigated according to the controlled coupling factor. The results suggest that the system exhibits coexisting periodic and chaotic bursting with different firing patterns. Complex firing only occurs in the locally active area of the defined memristor, meanwhile the system shows a periodic oscillation in the passive area. Beyond this, the coupled neurons exhibit the specific phenomenon of attractor growing in the locally active region of the memristor. The circuit simulations by Power Simulation (PSIM) are included confirming the numerical simulations and theoretic analysis.</p>","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154049","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Bifurcation Analysis of a Predator–Prey Model with Alternative Prey and Prey Refuges","authors":"Wenzhe Cui, Yulin Zhao","doi":"10.1142/s0218127424500214","DOIUrl":"https://doi.org/10.1142/s0218127424500214","url":null,"abstract":"<p>In this paper, we study the codimensions of Hopf bifurcation and Bogdanov–Takens bifurcation of a predator–prey model with alternative prey and prey refuges, which was proposed by Chen <i>et al.</i> [2023]. The results show that the predator–prey model can undergo a supercritical Hopf bifurcation or a Bogdanov–Takens bifurcation of codimension two under certain parameter conditions. It means that there are some predator–prey models with an alternative prey and prey refuges which have a limit cycle or a homoclinic loop. Moreover, it is also shown that the codimension of Hopf bifurcation is at most one and codimension of Bogdanov–Takens bifurcation is at most two.</p>","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154043","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Bifurcation Analysis of a Discrete Amensalism Model","authors":"Xinli Hu, Hanghang Li, Fengde Chen","doi":"10.1142/s0218127424500202","DOIUrl":"https://doi.org/10.1142/s0218127424500202","url":null,"abstract":"<p>By using model discretization of the piecewise constant argument method, a discrete amensalism model with nonselective harvesting and Allee effect is formulated. The dynamic analysis of the model is studied and the existence and stability of the equilibrium point are discussed. The fold bifurcation and flip bifurcation at the equilibrium point of the system are proved by using the bifurcation theory and the center manifold theorem. In order to control flip bifurcation and restore the system to a stable state, a hybrid control strategy of parameter perturbation and state feedback is adopted. Finally, the effectiveness of the theoretical results and the control strategy is verified by numerical simulations.</p>","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154051","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Emergence of Hidden Strange Nonchaotic Attractors in a Rational Memristive Map","authors":"Premraj Durairaj, Sathiyadevi Kanagaraj, Zhigang Zheng, Anitha Karthikeyan, Karthikeyan Rajagopal","doi":"10.1142/s0218127424500172","DOIUrl":"https://doi.org/10.1142/s0218127424500172","url":null,"abstract":"<p>To exemplify the existence of hidden strange nonchaotic attractors (HSNAs) and transition mechanism, we consider a rational memristive map with additional force. We find that the four-torus bifurcates into the eight-torus through torus doubling as a function of the control parameter. Following that, the formation of strange nonchaotic attractors occurs when increasing the control parameter. As a result, it is clear that the suggested rational maps reach hidden chaotic attractors via HSNAs through the route of torus doubling to torus breakdown. The obtained dynamical transitions are validated further using bifurcation analysis and the largest Lyapunov exponents. In particular, the obtained HSNAs are confirmed through distinct statistical measures including 0–1 test and singular continuous spectrum.</p>","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154136","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"From 1D Endomorphism to Multidimensional Hénon Map: Persistence of Bifurcation Structure","authors":"V. N. Belykh, N. V. Barabash, D. A. Grechko","doi":"10.1142/s0218127424500263","DOIUrl":"https://doi.org/10.1142/s0218127424500263","url":null,"abstract":"<p>The renowned 2D invertible Hénon map turns into 1D noninvertible quadratic map when its leading parameter <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>b</mi></math></span><span></span> becomes zero. This well-known link was studied by Mira who demonstrated that the bifurcation set of Hénon diffeomorphism is similar to his “box-within-a-box” bifurcation structure of 1D endomorphism. In general, such similarity has not been strictly established, especially in multidimensional cases. In this paper, we proved that the Mira bifurcation structure of a quadratic noninvertible map persists when the parameter increases from zero and the map turns into an invertible multidimensional generalized Hénon map. The changes of periodic and homoclinic orbits and chaotic attractors at this transition are described. We proved the existence of Newhouse regions is different from those Mira boxes that accumulate to the homoclinic bifurcations.</p>","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}